تكلم مع الذكاء الاصطناعي
Deck 11: Section 5: Vectors and the Geometry of Space
ملء الشاشة (f)
سؤال
Find a set of parametric equations of the line that passes through the point 
and is parallel to the xy-plane and yz-plane.
A)
B)
C)
D)
E)
and is parallel to the xy-plane and yz-plane.A)
B)
C)
D)
E)
سؤال
A chute at the top of a grain elevator of a combine funnels the grain into a bin (see figure). Find the angle between two adjacent sides. Round your answer to one decimal place. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find an equation of a plane passing through the following three points. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine whether any of the lines given below are parallel or identical. 
A)
are parallel
B)
are identical
C)
are parallel
D)
are identical
E)
are parallel
A)
are parallelB)
are identicalC)
are parallelD)
are identicalE)
are parallel سؤال
Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection. 
A) The planes are neither parallel nor orthogonal, the angle of intersection is
.
B) The planes are parallel.
C) The planes are neither parallel nor orthogonal, the angle of intersection is
.
D) The planes are orthogonal.
A) The planes are neither parallel nor orthogonal, the angle of intersection is
.B) The planes are parallel.
C) The planes are neither parallel nor orthogonal, the angle of intersection is
.D) The planes are orthogonal.
سؤال
Determine whether the lines given below intersect, and, if so, find the point of intersection. 
A) The lines are parallel.
B) The lines intersect at
.
C) The lines intersect at
.
D) The lines intersect at
.
E) The lines are not parallel but do not intersect.
A) The lines are parallel.
B) The lines intersect at
.C) The lines intersect at
.D) The lines intersect at
.E) The lines are not parallel but do not intersect.
سؤال
Find a set of parametric equations of the line through the point 
parallel to the vector 
.
A)
B)
C)
D)
E)
parallel to the vector .A)
B)
C)
D)
E)
سؤال
Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection. 
A) The planes are neither parallel nor orthogonal, the angle of intersection is
.
B) The planes are neither parallel nor orthogonal, the angle of intersection is
.
C) The planes are orthogonal.
D) The planes are parallel.
A) The planes are neither parallel nor orthogonal, the angle of intersection is
.B) The planes are neither parallel nor orthogonal, the angle of intersection is
.C) The planes are orthogonal.
D) The planes are parallel.
سؤال
Find a set of parametric equations of the line through the points 
and 
.
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
سؤال
Find the distance between the planes given below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the distance between the point 
and the line given by the set of parametric equations 
.
A)
/11
B) 2
C)
/11
D) 4
E) 1
and the line given by the set of parametric equations .A)
/11B) 2
C)
/11D) 4
E) 1
سؤال
Find a set of symmetric equations of the line through the points 
and 
.
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
سؤال
Find an equation of a plane passing through the points 
and perpendicular to the plane 
.
A)
B)
C)
D)
E)
and perpendicular to the plane .A)
B)
C)
D)
E)
سؤال
Find a set of symmetric equations of the line through the point 
parallel to the vector 
.
A)
B)
C)
D)
E)
parallel to the vector .A)
B)
C)
D)
E)
سؤال
Determine whether the lines given below intersect, and, if so, find the point of intersection. 
A) The lines intersect at
.
B) The lines are parallel.
C) The lines intersect at
.
D) The lines intersect at
.
E) The lines are not parallel but do not intersect.
A) The lines intersect at
.B) The lines are parallel.
C) The lines intersect at
.D) The lines intersect at
.E) The lines are not parallel but do not intersect.
سؤال
Find the distance between the point 
and the plane 
.
A)
B)
C)
D)
E)
and the plane .A)
B)
C)
D)
E)
سؤال
Find an equation of a plane passing through the given point and perpendicular to the given vector. Point: 
Vector: 
A)
B)
C)
D)
E)
Vector: A)
B)
C)
D)
E)
سؤال
Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is at the point 
where 
. Also, at time t, the second insect is at the point 
where 
. Assume distances are given in inches. Find the distance between the two insects at time 
. Round your answer to two decimal places.
A)
inches
B)
inches
C)
inches
D)
inches
E)
inches
where . Also, at time t, the second insect is at the point where . Assume distances are given in inches. Find the distance between the two insects at time . Round your answer to two decimal places.A)
inchesB)
inchesC)
inchesD)
inchesE)
inches سؤال
Determine whether any of the lines given below are parallel or identical. 
A)
are identical
B)
are identical
C)
are identical
D)
are parallel
E)
are parallel
A)
are identicalB)
are identicalC)
are identicalD)
are parallelE)
are parallel سؤال
Find the set of parametric equations of the line through the point 
that is parallel to the line 
, 
,and 
.
A)
B)
C)
D)
E)
that is parallel to the line , ,and .A)
B)
C)
D)
E)
سؤال
Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is at the point 
where 
. Also, at time t, the second insect is at the point 
where 
. Assume distances are given in inches. How close do the insects get? Round your answer to two decimal places.
A)
inches
B)
inches
C)
inches
D)
inches
E)
inches
where . Also, at time t, the second insect is at the point where . Assume distances are given in inches. How close do the insects get? Round your answer to two decimal places.A)
inchesB)
inchesC)
inchesD)
inchesE)
inches
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العب
ملء الشاشة (f)
Deck 11: Section 5: Vectors and the Geometry of Space
1
Find a set of parametric equations of the line that passes through the point and is parallel to the xy-plane and yz-plane.
A)
B)
C)
D)
E)
and is parallel to the xy-plane and yz-plane.A)
B)
C)
D)
E)
2
A chute at the top of a grain elevator of a combine funnels the grain into a bin (see figure). Find the angle between two adjacent sides. Round your answer to one decimal place.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Find an equation of a plane passing through the following three points.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Determine whether any of the lines given below are parallel or identical.
A) are parallel
B) are identical
C) are parallel
D) are identical
E) are parallel
A)
are parallelB)
are identicalC)
are parallelD)
are identicalE)
are parallel فتح الحزمة
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5
Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection.
A) The planes are neither parallel nor orthogonal, the angle of intersection is .
B) The planes are parallel.
C) The planes are neither parallel nor orthogonal, the angle of intersection is .
D) The planes are orthogonal.
A) The planes are neither parallel nor orthogonal, the angle of intersection is
.B) The planes are parallel.
C) The planes are neither parallel nor orthogonal, the angle of intersection is
.D) The planes are orthogonal.
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6
Determine whether the lines given below intersect, and, if so, find the point of intersection.
A) The lines are parallel.
B) The lines intersect at .
C) The lines intersect at .
D) The lines intersect at .
E) The lines are not parallel but do not intersect.
A) The lines are parallel.
B) The lines intersect at
.C) The lines intersect at
.D) The lines intersect at
.E) The lines are not parallel but do not intersect.
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7
Find a set of parametric equations of the line through the point parallel to the vector .
A)
B)
C)
D)
E)
parallel to the vector .A)
B)
C)
D)
E)
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8
Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection.
A) The planes are neither parallel nor orthogonal, the angle of intersection is .
B) The planes are neither parallel nor orthogonal, the angle of intersection is .
C) The planes are orthogonal.
D) The planes are parallel.
A) The planes are neither parallel nor orthogonal, the angle of intersection is
.B) The planes are neither parallel nor orthogonal, the angle of intersection is
.C) The planes are orthogonal.
D) The planes are parallel.
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9
Find a set of parametric equations of the line through the points and .
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
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10
Find the distance between the planes given below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Find the distance between the point and the line given by the set of parametric equations .
A) /11
B) 2
C) /11
D) 4
E) 1
and the line given by the set of parametric equations .A)
/11B) 2
C)
/11D) 4
E) 1
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12
Find a set of symmetric equations of the line through the points and .
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
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13
Find an equation of a plane passing through the points and perpendicular to the plane .
A)
B)
C)
D)
E)
and perpendicular to the plane .A)
B)
C)
D)
E)
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14
Find a set of symmetric equations of the line through the point parallel to the vector .
A)
B)
C)
D)
E)
parallel to the vector .A)
B)
C)
D)
E)
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15
Determine whether the lines given below intersect, and, if so, find the point of intersection.
A) The lines intersect at .
B) The lines are parallel.
C) The lines intersect at .
D) The lines intersect at .
E) The lines are not parallel but do not intersect.
A) The lines intersect at
.B) The lines are parallel.
C) The lines intersect at
.D) The lines intersect at
.E) The lines are not parallel but do not intersect.
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16
Find the distance between the point and the plane .
A)
B)
C)
D)
E)
and the plane .A)
B)
C)
D)
E)
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17
Find an equation of a plane passing through the given point and perpendicular to the given vector. Point: Vector:
A)
B)
C)
D)
E)
Vector: A)
B)
C)
D)
E)
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18
Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is at the point where . Also, at time t, the second insect is at the point where . Assume distances are given in inches. Find the distance between the two insects at time . Round your answer to two decimal places.
A) inches
B) inches
C) inches
D) inches
E) inches
where . Also, at time t, the second insect is at the point where . Assume distances are given in inches. Find the distance between the two insects at time . Round your answer to two decimal places.A)
inchesB)
inchesC)
inchesD)
inchesE)
inches فتح الحزمة
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19
Determine whether any of the lines given below are parallel or identical.
A) are identical
B) are identical
C) are identical
D) are parallel
E) are parallel
A)
are identicalB)
are identicalC)
are identicalD)
are parallelE)
are parallel فتح الحزمة
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20
Find the set of parametric equations of the line through the point that is parallel to the line , ,and .
A)
B)
C)
D)
E)
that is parallel to the line , ,and .A)
B)
C)
D)
E)
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21
Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is at the point where . Also, at time t, the second insect is at the point where . Assume distances are given in inches. How close do the insects get? Round your answer to two decimal places.
A) inches
B) inches
C) inches
D) inches
E) inches
where . Also, at time t, the second insect is at the point where . Assume distances are given in inches. How close do the insects get? Round your answer to two decimal places.A)
inchesB)
inchesC)
inchesD)
inchesE)
inches فتح الحزمة
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