Choose the one alternative that best completes the statement or answers the question.
-Which of the following vectors is orthogonal to $20 \mathbf { i } - 8 \mathbf { j }$ ?
A) $\mathbf { w } = 4 i + 3 j$
B) $w = 15 i - 6 j$
C) $\mathbf { w } = - 10 \mathbf { i } - 25 \mathrm { j }$
D) $w = 20 i + 4 j$

Question

Quizplus · Accepted Answer

The dot product of two orthogonal vectors is zero. So, we need to find the vector whose dot product with $20 \mathbf { i } - 8 \mathbf { j }$ is zero. The dot product of $20 \mathbf { i } - 8 \mathbf { j }$ and $- 10 \mathbf { i } - 25 \mathrm { j }$ is $$(20)(-10) + (-8)(-25) = 0$$So, $- 10 \mathbf { i } - 25 \mathrm { j }$ is orthogonal to $20 \mathbf { i } - 8 \mathbf { j }$.

Choose the One Alternative That Best Completes the Statement or Answers