Chapter 9.5, Problem 16AYU

To determine

To find:

a. The dot product $v\cdot w$ .

b. The angle between $v$ and $w$ .

c. State whether the vectors are parallel, orthogonal or neither.

Answer to Problem 16AYU

Solution:

a. 0

b. ${90}^{°}$

c. Orthogonal.

Explanation of Solution

Given:

  $v=i,w=-3j$

Calculation:

a. $v\cdot w=1(0)+0(-3)=0$

b. $\Vert v\Vert =\sqrt{{(1)}^2}=\sqrt{1}=1$

  $\Vert w\Vert =\sqrt{{(0)}^2+{(-3)}^2}=\sqrt{9}=3$

  $\cos \theta =\frac{v\cdot w}{\Vert v\Vert \Vert w\Vert }=\frac{0}{1(3)}=0$

  $\theta ={\cos }^{-1}(0)={90}^{°}$

c. The two vectors are orthogonal to each other.