The projection of the vector a=2 +3 +2 k on the vector b=i+2 j+k … - Vidyadip

MCQ

The projection of the vector $\vec{a}=2 \hat{\imath}+3 \hat{\jmath}+2 \hat{k}$ on the vector $\vec{b}=\hat{i}+2 \hat{j}+\hat{k}$ is

✓
$\frac{10}{\sqrt{6}}$
B
$\frac{10}{\sqrt{3}}$
C
$\frac{5}{\sqrt{6}}$
D
$\frac{5}{\sqrt{3}}$

✓

Answer

Correct option: A.

$\frac{10}{\sqrt{6}}$

(a): We have, $\vec{a}=2 \hat{i}+3 \hat{j}+2 \hat{k}$ and $\vec{b}=\hat{i}+2 \hat{j}+\hat{k}$
$
\therefore \quad \vec{a} \cdot \vec{b}=(2 \hat{i}+3 \hat{j}+2 \hat{k}) \cdot(\hat{i}+2 \hat{j}+\hat{k})=2+6+2=10
$
and $|\vec{b}|=\sqrt{1^2+2^2+1^2}=\sqrt{6}$
Hence, projection of $\vec{a}$ on $\vec{b}$ is $\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}=\frac{10}{\sqrt{6}}$.

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