Question

The vectors $\overline{a}=x\hat{i}-2\hat{j}+5\hat{k}$ and $\overline{b}=\hat{i}+y\hat{j}-z\hat{k}$are collinear if

• A. $x=1$, $y=-2$, $z=-5$
• B. $x=1/2$, $y=-4$, $z=-10$
• C. $x=-1/2$, $y=4$, $z=-10$
• D. $x=-1$, $y=2$, $z=5$

Answer 1

The correct option is A $x=1$, $y=-2$, $z=-5$

we have, $\overrightarrow{a}=x\hat{i}-x\hat{j}+5\hat{k}$ and $\overrightarrow{b}=\hat{i}+y\hat{j}-z\hat{k}$

Now, to have collinearity,

both vectors will be identical.

$\therefore x=1,y=-2,$ and $z=-5$ Ans