Question

6.If Å x B = B x Ă, then angle between A & B is

a.

`\pi / 2 \\`
b).

`\pi / 3`
c)π
d.

`\pi / 4`
​

Answer 1

`\theta = (\pi)/(4)`

Step-by-step explanation:

Given

`\uparrow A * B = B * \uparrow A`

Required

Determine the angle between A and B

We start with:

`\uparrow A * B = ABsin\theta`

and

`B * \uparrow A = ABcos\theta`

Subtract both equations

`ABsin\theta - ABcos\theta = \uparrow A B - B\uparrow A`

`ABsin\theta - ABcos\theta = 0`

`ABsin\theta = ABcos\theta`

Divide both sides by AB --- assume no null vectors

`sin\theta = cos\theta`

Divide both sides by
`cos\theta`

`(sin\theta)/(cos\theta) = (cos\theta)/(cos\theta)`

`tan\theta = 1`

Take tan inverse of both sides

`\theta = tan^(-1)(1)`

`\theta = 45^\circ`

Convert to radians

`\theta = (180)/(4)^\circ`

`\theta = (\pi)/(4)`