Question

The equation of the straight line passing through (1, 2, 3) and perpendicular to the plane x+2y-5z+9=0 is
[MP PET 1991]

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

The line passes through point (1,2,3) is $\frac{x-1}{a}=\frac{y-2}{b}=\frac{z-3}{c}$ and it is perpendicular to the plane x +2y - 5z + 9 = 0, therefore the line must be $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{-5}$ because $sin\theta =\frac{1.1+2.2+(-5)(-5)}{\sqrt{1^2+2^2+5^2}.\sqrt{1^2+2^2+5^2}}=1$
$\Rightarrow \theta ={90}^{\circ }$.