Question

For what values of x are the vectors u=⟨x,2,−3⟩ and v=⟨−1,3,2⟩ orthogonal?

Answer 1

The values of x for which the vectors u and v are orthogonal is x=0.

Step-by-step explanation:

To determine the values of x for which the vectors u and v are orthogonal, we need to find the dot product of u and v and set it equal to zero. The dot product of two vectors is given by the sum of the products of their corresponding components. In this case, the dot product of u and v is:

x * (-1) + 2 * 3 + (-3) * 2 = -x + 6 - 6 = -x

Setting this equal to zero, we have:

-x =0

Solving for x, we find that x=0.