Question

Given: $\overrightarrow{A}=i-2j,\overrightarrow{B}=2\hat{i}+3\hat{k}and\overrightarrow{C}=\hat{i}+\hat{j}$

Find component of vector $\overrightarrow{A}+\overrightarrow{B}$ along:

(i) x-axis

(ii) $\overrightarrow{C}$

• A. $3;\frac{1}{\sqrt{2}}$
• B. $2;\frac{1}{\sqrt{3}}$
• C. $3;\frac{1}{\sqrt{3}}$
• D. $2;\frac{1}{\sqrt{2}}$

Answer 1

The correct option is A $3;\frac{1}{\sqrt{2}}$

Given $\overrightarrow{A}=\hat{i}-2\hat{j}$ and $\overrightarrow{B}=2\hat{i}+3\hat{k}$
$A+B=(\hat{i}-2\hat{j})+(2\hat{i}+3\hat{k})=3\hat{i}-2\hat{j}+3\hat{k}$
i) Component of $\overrightarrow{A}+\overrightarrow{B}$ along x-axis is 3.
ii) Component of $\overrightarrow{A}+\overrightarrow{B}$ along $\overrightarrow{C}$ is given by
$Rcos\theta =\frac{\overrightarrow{R}.\overrightarrow{C}}{C}=\frac{(3\hat{i}-2\hat{j}+3\hat{k}).(\hat{i}+\hat{j})}{\sqrt{1^2+1^2}}=\frac{3-2}{\sqrt{2}}=\frac{1}{\sqrt{2}}$