Question

Find the value of p, if the lines given by the following equations are at right angles.

(2-x)/4 = (8y - 16)/2p (z-3)/2

(6 6x)/3p = (y - 7) = (6-z)/10

Answer 1

Given: Two lines: (2-x)/4 = (8y - 16)/2p = (z-3)/2  and (6+6x)/3p = (y - 7) = (6-z)/10

To find: Value of p.

Solution:

• As we have given that both the lines are perpendicular to each other, so the direction ratios relation will be:

              a1a2 + b1b2 + c1c2 = 0

• Rewriting equation in simpler form, we get:

              (x-2)/-4 = (y - 2)/1p/4 = (z-3)/2    and    (x+1)/1p/2 = (y - 7) = (z-6)/-10

• Now, according to formula, we have:

              -4 x 1/2 + p/4 x 1 + 2 x (-10) = 0

• Now solving further, we get:

              -2 + p/4 -20 = 0

              p/4 = 22

              p = 88

Answer:

                    So the value of p is 88.