Question

If the line passes through the points P(6, -1, 2), Q(8, -7, 2λ) and R(5, 2, 4) then value of λ is ______.

Options

• - 3

• 0

• - 1

• 2

Answer 1

If the line passes through the points P(6, -1, 2), Q(8, -7, 2λ) and R(5, 2, 4) then value of λ is - 1.

Explanation:

Equation of the line passes through the points P(6, -1, 2) and Q(8, -7, 2λ)

`=> (x - 6)/(8 - 6) = (y + 1)/(- 7 + 1) = (z + 2)/(2lambda - 2)`

`=> (x - 6)/2 = (y + 1)/(- 6) = (z - 2)/(2lambda - 2)`    ...(i)

Line (i) passes through point R (5, 2, 4)

∴ `(5 - 6)/2 = (2 + 1)/(- 6) = (4 - 2)/(2lambda - 2)`

`=> - 1/2 = 3/(- 6) = 2/(2lambda - 2)`

`=> 2/(2lambda - 2) = - 1/2`

`=> 1/(lambda - 1) = - 1/2`

`=> lambda - 1 = - 2`

`=> lambda = - 1`