Question

Given u = −5i + 8j and v = 56i + 35j, are u and v parallel or orthogonal? Explain.

The vectors are orthogonal because cos θ = 1.

The vectors are orthogonal because u ⋅ v = 0.

The vectors are parallel because cos θ = 1.

The vectors are parallel because u ⋅ v = 0.

Answer 1

Explanation:

To determine if the vectors u and v are parallel or orthogonal, we can calculate their dot product. If the dot product is zero, the vectors are orthogonal. If the dot product is nonzero, the vectors are parallel if and only if one vector is a scalar multiple of the other.

The dot product of u and v is:

u ⋅ v = (-5)(56) + (8)(35) = -280 + 280 = 0

Since the dot product is zero, we can conclude that u and v are orthogonal.

Therefore, the correct answer is:

The vectors are orthogonal because u ⋅ v = 0.