Q. Let $\overrightarrow{a}=5\hat{i}-\hat{j}-3\hat{k}$ and $\overrightarrow{b}=\hat{i}+3\hat{j}+5\hat{k}$ be two vectors. Then which one of the following statements is TRUE?
A) Projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ is $\frac{-13}{\sqrt{35}}$ and the direction of the projection vector is opposite to the direction of $\overrightarrow{b}$
B) Projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ is $\frac{-17}{\sqrt{35}}$ and the direction of the projection vector is opposite to the direction of $\overrightarrow{b}$
C) Projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ is $\frac{17}{\sqrt{35}}$ and the direction of the projection vector is opposite to the direction of $\overrightarrow{b}$
D) Projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ is $\frac{13}{\sqrt{35}}$ and the direction of the projection vector is opposite to the direction of $\overrightarrow{a}$
Explanation
The correct answer is Option A: Projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ is $\frac{-13}{\sqrt{35}}$ and the direction of the projection vector is opposite to the direction of $\overrightarrow{b}$.
A detailed explanation for this question is being prepared.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.