Question

The velocity of a particle is $\overset{\rightarrow}{v}$ = 6$\widehat{i}$ + 2$\widehat{j}$ – 2$\widehat{k}$. The component of the velocity of a particle parallel to vector $\overset{\rightarrow}{a}$= $\widehat{i}$ + $\widehat{j}$ + $\widehat{k}$in vector form is-

• A. 6$\widehat{i}$ + 2$\widehat{j}$ + 2$\widehat{k}$
• B. 2$\widehat{i}$+ 2$\widehat{j}$ + 2$\widehat{k}$
• C. $\widehat{i}$+$\widehat{j}$ + $\widehat{k}$
• D. 6$\widehat{i}$ + 2$\widehat{j}$ – 2$\widehat{k}$

Answer 1

Answer: (B)

2$\widehat{i}$+ 2$\widehat{j}$ + 2$\widehat{k}$

Answer 2

Component of $\overset{\rightarrow}{v}$along $\overset{\rightarrow}{a}$= $(\overset{\rightarrow}{v}.\widehat{a})$

= ($6\widehat{i}$ + $2\widehat{j}$ – $2\widehat{k}$). $\frac{\left( \widehat{i} + \widehat{j} + \widehat{k} \right)}{\sqrt{3}}$

= $\frac{6 + 2 - 2}{\sqrt{3}}$ = $\frac{6}{\sqrt{3}}$ = 2$\sqrt{3}$

In vector form = (2$\sqrt{3}$) $\widehat{a}$

= 2 $\sqrt { 3 }$ $\frac{\left( \widehat{i} + \widehat{j} + \widehat{k} \right)}{\sqrt{3}}$

= 2 $\left( \widehat{i} + \widehat{j} + \widehat{k} \right)$