Let α→=5i^−j^−3k^ and b→=i^+3j^+5k^ be two vectors. Then which one of the following statements is TRUE?

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

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Projection of $\vec{a} on \vec{b} is \frac{- 17}{\sqrt{35}}$ and the direction of the projection vector is same as of $\vec{b}$

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 $\vec{b}$

Projection of $\vec{a} on \vec{b} is \frac{17}{\sqrt{35}}$ and the direction of the projection vector is same as $\vec{b}$

answer is A.

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Projection of $\vec{a} on \vec{b} = | \vec{a} \cdot \hat{b} | = \frac{13}{\sqrt{35}}$ and projection vector is in opposite direction of $\vec{b}$ .