Question

Find the value of 'p' so that the lines: l1: 1-x/3 = 7y-14/2p = z-3/2 l2: 7-7x/3p = y-5/1 = 6-z/5
are at right angles.
Also, find the equations of the line passing through
(3,2, - 4) and parallel to line l1​

Answer 1

Answer:

Answer

l

1

=

3

1−x

=

p

7y−14

=

2

z−3

l

2

=

3p

7−7x

=

1

y−5

=

5

6−z

Given point P(3,2,−4)

Direction cosines;

l

1

=(3,p,2)

l

2

=(3p,1,5)

Given that both of the lines are ⊥.

Therefore, (3,p,2).(3p,1,5)=0

9p+p+10=0

10p=−10

p=−1

Therefore direction cosine of line dc

1

=(3,−1,2)

Direction cosine of line l

2

=(−3,1,5)

Required equation of line which is passing through P and parallel to l

1

=(3,2,−4)+λ(3,−1,2).