Question

Let $\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k}$ and $\vec{b}=\hat{i}+3 \hat{j}+5 \hat{k}$ be two vectors. Then which one of the following statements is TRUE ?

• A. Projection of $\vec{a}$ on $\vec{b}$ is $\frac{17}{\sqrt{35}}$ and the direction of the projection vector is same as of $\vec{b}$.
• B. Projection of $\vec{a}$ on $\vec{b}$ is $\frac{17}{\sqrt{35}}$ and the direction of the projection vector is opposite to the direction of $\vec{b}$
• C. Projection of $\vec{a}$ on $\vec{b}$ is $\frac{-17}{\sqrt{35}}$ and the direction of the projection vector is same as of $\vec{b}$.
• D. Projection of $\vec{a}$ on $\vec{b}$ is $\frac{-17}{\sqrt{35}}$ and the direction of the projection vector is opposite to the direction of $\vec{b}$.

Answer 1

Answer: (A)

$ \vec{ a }=5 \hat{ i }-\hat{ j }-3 \hat{ k } $
$ \vec{ b }=\hat{ i }-3 \hat{ j }+5 \hat{ k } $
$ \vec{ a } \cdot \hat{ b }=\frac{5-3-15}{\sqrt{35}}=-\frac{-13}{\sqrt{35}}$