IIT-JEE 2010 · Paper 1 · Mathematics Q30

← IIT-JEE 2010 · Paper 1

MathematicsSingle correct+3 / -1Question 30 of 84

Equation of the plane containing the straight line $\dfrac x2=\dfrac y3=\dfrac z4$ and perpendicular to the plane containing the straight lines $\dfrac x3=\dfrac y4=\dfrac z2$ and $\dfrac x4=\dfrac y2=\dfrac z3$ is

x+2y-2z=0

3x+2y-2z=0

x-2y+z=0

5x+2y-4z=0

Answer and worked solution

Official answer: C

Normal of the plane of the two lines.
$(3,4,2)\times(4,2,3)=(12-4,\ 8-9,\ 6-16)=(8,-1,-10).$

Required plane. It contains the direction $(2,3,4)$ and is perpendicular to that plane, so it also contains the direction $(8,-1,-10)$ . Its normal is
$(2,3,4)\times(8,-1,-10)=(-26,52,-26)\parallel(1,-2,1).$
It passes through the origin (which is on the first line): $x-2y+z=0$ .

(C)

Topics:Equation of a plane

← Previous question Next question →

IIT-JEE 2010 · Paper 1, Mathematics question 30