Question

If $\overline{OP}=2\overline{i}+3\overline{j}-\overline{k},\overline{OQ}=3\overline{i}-4\overline{j}+2\overline{k}$ then d.c's of $\overline{PQ}$ are

• A. $\frac{1}{\sqrt{59}}(-1,7,3)$
• B. $\frac{1}{\sqrt{59}}(1,-7,3)$
• C. $\frac{1}{\sqrt{59}}(1,7,-3)$
• D. $\frac{1}{\sqrt{59}}(1,-7,-3)$

Answer 1

Answer: (B)

$\frac{1}{\sqrt{59}}(1,-7,3)$

We have,

$\overline{OP}=2\overline{i}+3\overline{j}-\overline{k}\overline{OQ}=3\overline{i}-4\overline{j}+2\overline{k}$

$\overline{PQ}=\overline{OQ}-\overline{OP}$

$=3\overline{i}-4\overline{j}+2\overline{k}-\left(2\overline{i}+3\overline{j}-\overline{k}\right)$

$\overline{PQ}=\overline{i}-7\overline{j}+3\overline{k}$

$\left|\overline{PQ}\right|=\sqrt{59}$

$D.Cof\overline{PQ}=\frac{1}{\sqrt{59}}\left(1,-7,3\right)$

Then,

Option $B$ is correct anwer.