Question

A line with positive direction cosine passes through the point P(2, – 1, 2) and makes equal angles with coordinate axes. The line meets the plane 2x + y + z = 9 at Q. Then the length of line segment PQ is equal to

• A. 1
• B. $\sqrt{2}$
• C. $\sqrt{3}$
• D. 2

Answer 1

The correct option is C $\sqrt{3}$

Equation of line is $\frac{x-2}{1}=\frac{y+1}{1}=\frac{z-2}{1}=k\left(say\right)$
$\Rightarrow Q=(k+2,k-1,k+2)$ lies on 2x + y + z = 9
$\Rightarrow 2(k+2)+k-1+(k+2)=9$
$\Rightarrow k=1$
$\therefore Q=(3,0,3)PQ=\sqrt{1+1+1}=\sqrt{3}$
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