Chapter 6.4, Problem 84E

a.

To determine

Value of $\theta$ for given condition.

Answer to Problem 84E

When the angle between vector u and v is $90°$ .

Explanation of Solution

Given information:

  $u.v=0$

Formula used: -

  $u.v=\Vert u\Vert \Vert v\Vert \cos \theta$

  $u.v=\Vert u\Vert \Vert v\Vert \cos \theta$

When the angle will be $90°$ . Then, $\cos \theta$ will 0. Hence, $u.v$ will be zero.

b.

To determine

Value of $\theta$ for given condition.

Answer to Problem 84E

When the angle between vector u and v is between $0^{°}to90°$ .

Explanation of Solution

Given information:

  $u.v>0$

Formula used: -

  $u.v=\Vert u\Vert \Vert v\Vert \cos \theta$

  $u.v=\Vert u\Vert \Vert v\Vert \cos \theta$

When the angle is between $0^{°}to90°$ . Then, $\cos \theta$ will positive. Hence, $u.v$ will be positive.

c.

To determine

Value of $\theta$ for given condition.

Answer to Problem 84E

When the angle between vector u and v is greater than $90°$ .

Explanation of Solution

Given information:

Formula used: -

  $u.v=\Vert u\Vert \Vert v\Vert \cos \theta$

  $u.v=\Vert u\Vert \Vert v\Vert \cos \theta$

When the angle is greater than $90°$ . Then, $\cos \theta$ will negative. Hence, $u.v$ will be negative.