The projection of vector i on the vector i+j+2 k is: - Vidyadip

MCQ

The projection of vector $\hat{i}$ on the vector $\hat{i}+\hat{j}+2 \hat{k}$ is:

A
$\frac{1}{\sqrt{6}}$
B
$\sqrt{6}$
C
$\frac{2}{\sqrt{6}}$
D
$\frac{3}{\sqrt{6}}$

✓

Answer

Let, $\vec{a}=\hat{i}$ and $\vec{b}=\hat{i}+\hat{j}+2 \hat{k}$
We know that, projection of vector $\vec{a}$ on $\vec{b}=\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$
$
=\frac{\hat{i} \cdot(\hat{i}+\hat{j}+2 \hat{k})}{\sqrt{1^2+1^2+2^2}}=\frac{1}{\sqrt{6}}$

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