Write the projection of i + j + k along the vector j . - Vidyadip

Question

Write the projection of $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ along the vector $\hat{\text{j}}.$

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Answer

Projection of $\vec{\text{a}}$ on $\vec{\text{b}}=\frac{\vec{\text{a}}.\vec{\text{b}}}{\big|\vec{\text{b}}\big|}$
Projection of $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ along $\hat{\text{j}}$
$=\frac{\big(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}\big).\vec{\text{j}}}{|\vec{\text{j}}|}$
$=\frac{1}{1}$
$=1$

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