Question

A straight line $r=a+\lambda b$ meets the plane $r.n=0$ in $P$. The position vector of $P$ is

• A. $a+\frac{a.n}{b.n}b$
• B. $a+\frac{b.n}{a.n}b$
• C. $a-\frac{a.n}{b.n}b$
• D. None of these

Answer 1

The correct option is C $a-\frac{a.n}{b.n}b$

A straight line $r=a+\lambda b$ meets the plane $r.n=0$ in $P$ for which $\lambda$ is given by

$(a+\lambda b).n=0\Rightarrow \lambda =-\frac{a.n}{b.n}$

Thus, the position vector of $P$ is

$r=a-\frac{a.n}{b.n}b$ $[$ putting the value of $\lambda$ in $r=a+\lambda b]$