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Mathematics Question on Vector Algebra

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

A

835\frac {8}{\sqrt {35}}

B

839\frac {8}{\sqrt {39}}

C

814\frac {8}{\sqrt {14}}

D

14\sqrt {14}

Answer

814\frac {8}{\sqrt {14}}

Explanation

Solution

The correct answer is C:814\frac{8}{\sqrt{14}}
Given, a⃗=3i^−j^+5k^    \vec{a} =3 \hat{i} - \hat{j} + 5 \hat{k}\,\,\,\, and     b⃗=2i^+3j^+k^\,\,\,\,\vec{b} =2 \hat{i} + 3 \hat{j} + \hat{k}
Then, a⃗.b⃗=(3×2)+(−1×3)+5×1\vec{a}.\vec{b}=(3\times2)+(-1\times3)+5\times1
=b−3+5=8=b-3+5=8
The projection of a⃗\vec{a} on b⃗=a⃗.b⃗∣b⃗∣\vec{b} = \frac{\vec{a} . \vec{b}}{\left|\vec{b}\right|}
=814= \frac{8}{\sqrt{14}}
vector