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Vector Algebra question

2023 · 1 Feb · Shift 2 · Q27

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JEE Main
Mathematics
Vector Algebra
2023 · 1 Feb · Shift 2 · Q27

Vector Algebra question

2023 · 1 Feb · Shift 2 · Q27

JEE MainMathematicsVector AlgebraMCQ+4 / −1

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 $\frac{-13}{\sqrt{35}}$ and the direction of the projection vector is opposite to the direction of $\vec{b}$ .
B
Projection of $\vec{a}$ on $\vec{b}$ is $\frac{13}{\sqrt{35}}$ and the direction of the projection vector is opposite to the direction of $\vec{b}$ .
C
Projection of $\vec{a}$ on $\vec{b}$ is $\frac{13}{\sqrt{35}}$ and the direction of the projection vector is same as of $\vec{b}$ .
D
Projection of $\vec{a}$ on $\vec{b}$ is $\frac{-13}{\sqrt{35}}$ and the direction of the projection vector is same as of $\vec{b}$ .

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