Q131 / 160 · WBJEE 2009 · Physics

$\vec{A}$ and $\vec{B}$ are two vectors given by $\vec{A}=2 \hat{i}+3 \hat{j}$ and $\vec{B}=\hat{i}+\hat{j}$. The magnitude of the component of $\vec{A}$ along $\vec{B}$ is

  • Correct answer
    A
    $\frac{5}{\sqrt{2}}$
  • B
    $\frac{3}{\sqrt{2}}$
  • C
    $\frac{7}{\sqrt{2}}$
  • D
    $\frac{1}{\sqrt{2}}$

Solution

Magnitude of components of $\vec{A}$ along $\vec{B}=\frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}=\frac{(2 \hat{i}+3 \hat{j})(\hat{i}+\hat{j})}{\sqrt{2}}=\frac{5}{\sqrt{2}}$

Hence, the correct answer is option: 'A'.

Relevant Questions