For the vectors shown in the figure,find the magnitude and direction of the vector product ×
,assuming that the quantities shown are accurate to two significant figures.
A) 16, directed into the plane
B) 16, directed out of the plane
C) 45, directed on the plane
D) 45, directed into the plane
E) 45, directed out of the plane

Question

For the vectors shown in the figure,find the magnitude and direction of the vector product  × 
,assuming that the quantities shown are accurate to two significant figures. 
A) 16, directed into the plane 
B) 16, directed out of the plane 
C) 45, directed on the plane 
D) 45, directed into the plane 
E) 45, directed out of the plane

Quizplus · Accepted Answer

To find the vector product of two vectors A and B, we use the formula: 
A x B = |A| |B| sin(theta) n
where |A| and |B| are the magnitudes of the vectors, theta is the angle between them, and n is a unit vector perpendicular to both A and B, following the right-hand rule.
In this case, the magnitudes of both vectors are given as 11, and the angle between them is 90 degrees (since they are perpendicular). Therefore, sin(theta) = 1, and the magnitude of the vector product is |A x B| = |11| |11| |sin(90)| = 121. 
Since A x B is perpendicular to both A and B, it must be on the plane defined by both vectors. Using the right-hand rule, we can see that A x B is directed out of the plane, which corresponds to answer choice E.

For the Vectors Shown in the Figure,find the Magnitude and Direction