Question 1

The distance from (5, 7, 10) to the xz-plane is
A) 5
B) 7
C) 10
D) 13.190906
E) 8.602325

Accepted Answer

The distance from a point to the xz-plane is given by the absolute value of the y-coordinate of the point, which in this case is 7.

Question 2

Find the distance from the surface  to (9, 0, 0).

Accepted Answer

The answer of Find the distance from the surface ...

Question 3

Find the distance from the sphere  to the point (0, 0, 11).

Accepted Answer

The answer of Find the distance from the sphere ...

Question 4

Complete the square to identify the center and radius of the following sphere:

Accepted Answer

The answer of Complete the square to identify the center...

Question 5

Find the equation of the sphere with a diameter whose endpoints are  and  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The center of the sphere is the midpoint of the given endpoints, which is:
$$\frac{1}{2}(11ead0bc_8e4c_ac47_99a0_637f8228c9b6_TB6988_11+11ead0bc_8e4c_d358_99a0_4bc6799adb6c_TB6988_11) = 11ead0bc_8e4c_fa6a_99a0_19e2dc63d291_TB6988_11$$

The radius of the sphere is half of the distance between the given endpoints, which is:
$$\frac{1}{2}\sqrt{(11ead0bc_8e4c_d358_99a0_4bc6799adb6c_TB6988_11-11ead0bc_8e4c_ac47_99a0_637f8228c9b6_TB6988_11)^2} = \frac{1}{2}\sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2}$$

where $\Delta x$, $\Delta y$ and $\Delta z$ are the differences in x, y and z coordinates between the endpoints. Plugging in the values, we get:
$$\frac{1}{2}\sqrt{(3471)^2+(8e-4c)^2+(e-5)^2} = \frac{1}{2}\sqrt{12064448042_TB6988_11}$$

Therefore, the equation of the sphere is:
$$(x-11ead0bc_8e4c_fa6a_99a0_19e2dc63d291_TB6988_11)^2+(y-11ead0bc_8e4c_fa6a_99a0_19e2dc63d291_TB6988_11)^2+(z-11ead0bc_8e4c_fa6a_99a0_19e2dc63d291_TB6988_11)^2 = \frac{1}{4}\sqrt{12064448042_TB6988_11}$$

Simplifying and expressing in hexadecimal format, we get:
$$(x-11ead0bc_8e4c_fa6a_99a0_19e2dc63d291_TB6988_11)^2+(y-11ead0bc_8e4c_fa6a_99a0_19e2dc63d291_TB6988_11)^2+(z-11ead0bc_8e4c_fa6a_99a0_19e2dc63d291_TB6988_11)^2 = 4429ca66_TB6988_16$$

Which matches with option B: 11ead0bc_8e4c_fa6a_99a0_2fc58f2bd2d6_TB6988_11.

Question 6

The distance from (2, -1, -4) to the xy-plane is

Accepted Answer

The answer of The distance from (2, -1, -4) to...

Question 7

Complete the square to identify the center and radius of the following sphere:

Accepted Answer

The answer of Complete the square to identify the center...

Question 8

Find the equation of the sphere with a diameter whose endpoints are  and  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The center of the sphere is the midpoint of the given diameter, which is 
$$\frac{1}{2}[(11ead0bc_8e4c_1000_99a0_f1ea589aef47_TB6988_11 + 11ead0bc_8e4c_3711_99a0_7ba88c0fd222_TB6988_11)]$$
$$= \frac{1}{2}(11ead0bc_8e4c_4711_99a0_34a8b436c084_TB6988_11)$$
$$= 11ead0bc_8e4c_8534_99a0_81c7e6d28605_TB6988_11$$
 
The radius of the sphere is half the distance between the two endpoints, which is 
$$\frac{1}{2}[\sqrt{(11ead0bc_8e4c_3711_99a0_7ba88c0fd222_TB6988_11 - 11ead0bc_8e4c_1000_99a0_f1ea589aef47_TB6988_11)^2}]$$ $$= \frac{1}{2}\sqrt{(0)^2 + (2711)^2 + (0)^2}$$
$$ = 1355.5$$ 
Therefore, the equation of the sphere is 
$$(x - 11ead0bc_8e4c_8534_99a0_81c7e6d28605_TB6988_11)^2 + (y - 11ead0bc_8e4c_8534_99a0_81c7e6d28605_TB6988_11)^2 + (z - 11ead0bc_8e4c_8534_99a0_81c7e6d28605_TB6988_11)^2 = (1355.5)^2$$ 
which is equivalent to choice C.

Question 9

The equation for a cylinder with radius 5 oriented symmetrically about the y-axis is

Accepted Answer

The answer of The equation for a cylinder with radius...

Question 10

What is the radius of the sphere

Accepted Answer

The answer of What is the radius of the sphere...

Question 11

What is the radius of the sphere

Accepted Answer

The answer of What is the radius of the sphere...

Question 12

A rectangular box has a corner at the origin and corners at (0, 0, 4), (0, 7, 0), (9, 0, 0), (4, 7, 0), (4, 0, 9), and (0, 7, 9). The other corner is

Accepted Answer

The answer of A rectangular box has a corner at...

Question 13

The distance from (6, 8, 11) to the yz-plane is
A) 6
B) 8
C) 11
D) 14.866069
E) 10

Accepted Answer

The distance from a point to the yz-plane is given by the absolute value of the x-coordinate of the point, which is 6 in this case.

Quiz 11: Three-Dimensional Space; Vectors

The distance from (5, 7, 10) to the xz-plane is

Find the distance from the surface to (9, 0, 0).

Find the distance from the sphere to the point (0, 0, 11).

Complete the square to identify the center and radius of the following sphere:

Find the equation of the sphere with a diameter whose endpoints are and .

The distance from (2, -1, -4) to the xy-plane is

Complete the square to identify the center and radius of the following sphere:

Find the equation of the sphere with a diameter whose endpoints are and .

The equation for a cylinder with radius 5 oriented symmetrically about the y-axis is

What is the radius of the sphere

What is the radius of the sphere

A rectangular box has a corner at the origin and corners at (0, 0, 4), (0, 7, 0), (9, 0, 0), (4, 7, 0), (4, 0, 9), and (0, 7, 9). The other corner is

The distance from (6, 8, 11) to the yz-plane is