Skip to content
dronacharya.ai
← IIT-JEE 2009 · Paper 2
MathematicsSingle correct+3 / -1Question 21 of 57

IIT-JEE 2009 · Paper 2, Mathematics question 21

A line with positive direction cosines passes through the point P(2,−1,2)P(2,-1,2) and makes equal angles with the coordinate axes. The line meets the plane
2x+y+z=92x+y+z=9
at point QQ. The length of the line segment PQPQ equals

Choose one option
Answer and worked solution

Official answer: C

Line. Equal angles with the axes and positive direction cosines: direction (1,1,1)(1,1,1). Points (2+t, −1+t, 2+t)(2+t,\,-1+t,\,2+t).

Meet the plane. 2(2+t)+(−1+t)+(2+t)=5+4t=92(2+t)+(-1+t)+(2+t)=5+4t=9, so t=1t=1 and Q=(3,0,3)Q=(3,0,3).

Length. PQ=1+1+1=3PQ=\sqrt{1+1+1}=\sqrt3.

(C)

Topics:Equation of a line in spaceDirection cosines and ratios
← Previous questionNext question →