Question

Let $a=\overline{i}+\overline{j}-\overline{k},\overline{b}=\overline{5i}-\overline{3j}-\overline{3k},\overline{c}=\overline{3i}-j-\overline{2k}.$ If collinear with $\overline{c}$ and $|\overline{r}|=|\overline{a}+\overline{b}|.$ Then $\overline{r}$ equals :

• A. $\pm \overline{3c}$
• B. $\pm \frac{3}{2}\overline{3c}$
• C. $\pm \overline{2c}$
• D. $\pm \frac{3}{2}\overline{4c}$

Answer 1

The correct option is C $\pm \overline{2c}$

We have,

$\overrightarrow{a}=\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k}$

$\overrightarrow{b}=5\overrightarrow{i}-3\overrightarrow{j}-3\overrightarrow{k}$

$\overrightarrow{c}=3\overrightarrow{i}-\overrightarrow{j}-2\overrightarrow{k}$

Given that,

It ius collinear with $$\overrightarrow{c}$$.

Then,

$\left|\overrightarrow{r}\right|=|\overrightarrow{a}+\overrightarrow{b}|$

$=|\overrightarrow{i}+\overrightarrow{j}-\overrightarrow{k}+5\overrightarrow{i}-3\overrightarrow{j}-3\overrightarrow{k}|$

$=|6\overrightarrow{i}-2\overrightarrow{j}-4\overrightarrow{k}|$

$=2|3\overrightarrow{i}-\overrightarrow{j}-2\overrightarrow{k}|$

$=\pm 2\overrightarrow{c}$

Hence, this is the answer.