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Mathematics Question on Vector Algebra

The projection of a⃗=5i^−j^+3k^\vec{a} = 5\hat{i} - \hat{j} + 3 \hat{k} on b⃗=2i^+j^−k^\vec{b} = 2 \hat{i} + \hat{j} - \hat{k} is

A

6

B

6\sqrt{6}

C

3\sqrt{3}

D

None of these

Answer

6\sqrt{6}

Explanation

Solution

Projection of a⃗\vec{a} on b⃗\vec{b} is =a⃗.b⃗∣b⃗∣=10−1−34+1+1=66=6= \frac{\vec{a}.\vec{b}}{\left|\vec{b}\right|} = \frac{10-1-3}{\sqrt{4+1+1}} =\frac{6}{\sqrt{6}} = \sqrt{6}