Question

If the vectors $2\overline{i}-3\overline{j}+6\overline{k},\overline{b}$ are collinear and $|\overline{b}|=14$ then $\overline{b}=$

• A. $\frac{1}{7}(-2\overline{i}+3\overline{j}+6\overline{k})$
• B. $\pm (4\overline{i}-6\overline{j}+12\overline{k})$
• C. $6\overline{i}-9\overline{j}+18\overline{k}$
• D. $\frac{1}{7}(2\overline{i}-3\overline{j}+6\overline{k})$

Answer 1

The correct option is B $\pm (4\overline{i}-6\overline{j}+12\overline{k})$

$\overrightarrow{a}=2i-3j+6k$ and $\overrightarrow{a}$ and $\overrightarrow{b}$ are collinear, then
$\overrightarrow{b}=b\left(\frac{\overrightarrow{a}}{|a|}\right)$
$=14\left(\frac{2i-3j+6k}{\sqrt{4+9+36}}\right)$
$=14\left(\frac{2i-3i+6k}{\sqrt{49}}\right)$
$=14\left(\frac{2i-3i+6k}{7}\right)$
$=2(2i-3j+6k)$
$=4i-6j+12k$