Vector $\vec { A }$ is along the +x-axis and vector $\overrightarrow { \mathbf { B } }$ is along the +y-axis. Which one of the following statements is correct with respect to these vectors?
A) The x component of vector $\vec { A }$ is equal to the x component of vector $\overrightarrow { \mathbf { B } }$ .
B) The y component of vector $\vec { A }$ is equal to the y component of vector $\overrightarrow { \mathbf { B } }$ .
C) The x component of vector $\vec { A }$ is equal to the y component of vector $\overrightarrow { \mathbf { B } }$ .
D) The y component of vector $\vec { A }$ is equal to the x component of vector $\overrightarrow { \mathbf { B } }$ .

Question

Quizplus · Accepted Answer

The x component of vector $\vec{A}$ is given by the number in front of the unit vector $\hat{i}$ and is equal to the magnitude of the projection of the vector onto the x-axis. Since vector $\vec{A}$ is along the +x-axis, its projection onto the y-axis is 0, which means that its y component is also 0. Therefore, the y component of vector $\vec{A}$ is equal to 0 and is not equal to the y component of vector $\overrightarrow{\mathbf{B}}$, which is given by the number in front of the unit vector $\hat{j}$ and is equal to the magnitude of the projection of the vector onto the y-axis. Since vector $\overrightarrow{\mathbf{B}}$ is along the +y-axis, its projection onto the x-axis is 0, which means that its x component is also 0. Therefore, the x component of vector $\overrightarrow{\mathbf{B}}$ is equal to 0 and is not equal to the y component of vector $\vec{A}$. Therefore, the only correct statement is that the y component of vector $\vec{A}$ is equal to the x component of vector $\overrightarrow{\mathbf{B}}$, which are both equal to 0.

Vector A⃗\vec { A }A Is Along the +X-Axis and Vector B→\overrightarrow { \mathbf { B } }B

Vector $\vec { A }$ Is Along the +X-Axis and Vector $\overrightarrow { \mathbf { B } }$