Question

Let A be a point on the line $\overrightarrow{r}=(1-3\mu )\hat{i}+(\mu -1)\hat{j}+(2+5\mu )\hat{k}$ and $B(3,2,6)$ be a point in the space. Then the value of $\mu$ for which the vector $\overline{AB}$ is parallel to the plane $x-4y+3z=1$ is?

• A. $\frac{1}{2}$
• B. $-\frac{1}{4}$
• C. $\frac{1}{4}$
• D. $\frac{1}{8}$

Answer 1

The correct option is C $\frac{1}{4}$

Let point A is
$(1-3\mu )\hat{i}+(\mu -1)\hat{j}+(2+5\mu )\hat{k}$
and point B is $(3,2,6)$
then $\overline{AB}=(2+3\mu )\hat{i}+(3-\mu )\hat{j}+(4-5\mu )\hat{k}$
which is parallel to the plane $x-4y+3z=1$
$\therefore 2+3\mu -12+4\mu +12-15\mu =0$
$8\mu =2$
$\mu =\frac{1}{4}$.