Question

Consider three vectors $\overline{p}=\hat{i}+\hat{j}+\hat{k},q=2\hat{i}+4\hat{j}-\hat{k}$ and $\overline{r}=\hat{i}+\hat{j}+3\hat{k}$ and let $\overline{s}$ be a unit vector then $\overline{p},\overline{q}$ and $\overline{r}$ are

• A. Linearly dependent
• B. Can form the sides of a possible triangle
• C. Such that the vectors $(\overline{q}-\overline{r})$ is orthogonal to $\overline{p}$
• D. None of the above

Answer 1

Answer: (C)

Such that the vectors $(\overline{q}-\overline{r})$ is orthogonal to $\overline{p}$

$q-r$

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

Now $(q-r).\left(\overline{r}\right)$

$=(\overline{i}+3\overline{j}-4\overline{k}).(\overline{i}+\overline{j}+\overline{k})$

$=1+3-4$

$=0$

Hence correct option is $C$.