Question

use the dot product to determine whether v and w are orthogonal. v = 2i, w = -2j select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. they are not orthogonal because the dot product is \boxed{}. b. they are orthogonal because the dot product is \boxed{}.

Explanation:

Step1: Write vectors in component form

$\mathbf{v} = \langle 2, 0
angle$, $\mathbf{w} = \langle 0, -2
angle$

Step2: Calculate the dot product

$\mathbf{v} \cdot \mathbf{w} = (2)(0) + (0)(-2) = 0 + 0 = 0$

Step3: Check orthogonality rule

Vectors are orthogonal if their dot product is 0.

Answer:

B. They are orthogonal because the dot product is 0.