Question

The figure below shows two vectors lying in the \(x y\) plane. Determine the signs of the \(x\) and \(y\) components of \(\overrightarrow{\mathrm{A}}, \overrightarrow{\mathrm{B}},\) and \(\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}},\) and place your answers in the following table.

Answer 1

A points up and to the left. This means its y-component is positive and its x-component is negative.

B points down and to the right. This means its y-component is negative and its x-component is positive.

A+B can be found by putting a copy of A at the tip of B and putting a copy of B at the tip of A. The arrowheads of these copies will meet somewhere in quadrant III. Now draw a vector from the origin to this arrowhead meeting point. That is the A+B vector. Since it points left and down, its x and y components are both negative.