Question

The component of vector $3\hat{i}+4\hat{j}$ along vector $\hat{i}+\hat{j}$ is

• A. $\frac{1}{2}(\hat{j}+\hat{i})$
• B. $\frac{3}{2}(\hat{j}+\hat{i})$
• C. $\frac{5}{2}(\hat{j}+\hat{i})$
• D. $\frac{7}{2}(\hat{j}+\hat{i})$

Answer 1

Answer: (D)

$\frac{7}{2}(\hat{j}+\hat{i})$

Component of $\overrightarrow{A}$ along $\overrightarrow{B}$ is $\frac{\overrightarrow{A}.\overrightarrow{B}}{B}\hat{B}$
Hence, it is $\frac{(3\hat{i}+4\hat{j}).(\hat{i}+\hat{j})}{\sqrt{2}}\frac{\hat{i}+\hat{j}}{\sqrt{2}}=\frac{7}{2}(\hat{i}+\hat{j})$