If P(6,10,10),Q(1,0,-5),R(6,-10,`lamda`) are vertices of a triangle right angled at Q, then value of `lamda` is . .

Options

A. 0
B. 1
C. 3
D. 2

Answer

A

Explanation

In `Delta PQR` is right angled at `theta`
`PR^(2) = PQ^(2) + RQ^(2)`
`implies (6 - 6)^(2) + (-10 - 10)^(2) + (lambda - 10)^(2)`
`+ [(1- 6)^(2) + (0 - 10)^(2) + (-5 - 10)^(2)]`
`= [(1 - 6)^(2) + (0 + 10)^(2) + (-5 - lambda)^(2)]`
`implies 400 + lambda^(2) + 100 - 20 lambda = (25 + 100 + 225) + (25 + 100 + 25 + lambda^(2) + 10 lambda)`
`implies lambda^(2) = 20 lambda + 500 = 350 + 150 + 10 lambda + lambda^(2)`
`implies - 20 lambda = 10 lambda implies 30 lambda = 30`
`implies lambda = 0`