Question

Find the value of p such that the lines \(\frac{x+11}{4}=\frac{y+3}{-2}=\frac{z-3}{4} \,and \,\frac{x-3}{p}=\frac{y+12}{2}=\frac{z-3}{-12}\) are at right angles to each other.

(a) p=11

(b) p=12

(c) p=13

(d) p=4

The question was asked during an interview.

I'm obligated to ask this question of Three Dimensional Geometry in chapter Three Dimensional Geometry of Mathematics – Class 12

Answer 1

The correct choice is (c) p=13

To explain: We know that, if two lines are perpendicular to each other then,

\(a_1 a_2+b_1 b_2+c_1 c_2=0\)

i.e.4(p)+(-2)2+4(-12)=0

4p-4-48=0

4p=52

p=\(\frac{52}{4}\)=13.