Question

The component of $3\widehat{i} + 4\widehat{j}$ along $\widehat{i} + \widehat{j}$ -

• A. (a)$\frac{\widehat{i} + \widehat{j}}{2}$
• A. (b)$\frac{3}{2}(\widehat{i} + \widehat{j})$
• A. (c)$\frac{5}{2}(\widehat{i} + \widehat{j})$
• A. (d)$\frac{7}{2}(\widehat{i} + \widehat{j})$

Answer 1

(d)

Component of $\overset{\rightarrow}{A}$ along $\overset{\rightarrow}{B}$

=$\frac{\overset{\rightarrow}{A}.\overset{\rightarrow}{B}}{B} = \frac{3 + 4}{\sqrt{2}}$ = $\frac{7}{\sqrt{2}}$

In vector form = $\frac{7}{\sqrt{2}}$ $\widehat{B}$

= $\frac { 7 } { \sqrt { 2 } }$ $\left( \frac{\widehat{i} + \widehat{j}}{\sqrt{2}} \right)$=$\frac{7}{2}(\widehat{i} + \widehat{j})$