Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?

Question

Each of two vectors,  and  , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is  . Which possibility is correct?

Quizplus · Accepted Answer

Since both vectors lie along a coordinate axis in the xy plane, their dot product will be equal to the product of their magnitudes and directions along the common axis. Therefore, the dot product being positive means that both vectors have the same direction (either both positive or both negative) along the axis. Answer choice B is the only one that satisfies this condition, with one vector lying along the positive x axis and the other along the negative x axis.

Each of Two Vectors, and , Lies Along