Question

In: Physics

The vector product of vectors A⃗ and B⃗ has magnitude 20.0 m2 and is in the...

The vector product of vectors A⃗ and B⃗ has magnitude 20.0 m2 and is in the +z-direction. Vector A⃗ has magnitude 8.0 m and is in the −x-direction. Vector B⃗ has no x-component.

Part a : What is the magnitude of vector B⃗ ?

Part b:What is the direction angle θ of vector B⃗ measured from the +y-direction to the +z-direction?

Expert Solution

Concept :

Vector product of two vectors can be found by

A × B = |A| |B| sin(θ) n

|A| is the magnitude of vector A
|B| is the magnitude of vector B
θ is the angle between A and B
n is the unit vector at right angles to both A and B

And the direction of resultant vector given by Right hand rule :

Explanation:

a) Given that ,

has no x component
   must be in the -y direction in order for the vector product to be in the +z direction and A to be in -x direction. (from right hand rule )
Thus   , where B is the magnitude of vector
Also the angle between A and B is 900  (from right hand rule )

Magnitude of the vector product is given by

b) Direction angle θ of is 900 , as =

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