JEE Advanced | 2014Math miscellaneousHard

Question

From a point P(λ, λ, λ) perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = - x, z = - 1. If P is such that ∠QPR is a right angle, then the possible value(s) of λ is(are)

Options

A.√2
B.1
C.-1
D.-√2

Solution

       
= K         .....(i)
⇒ Q : (K, K, 1)
= m         .....(ii)
⇒ R : (-m, m, -1)
∵ PQ is perpendicular to line (i)
∴ (λ - K) + (λ - K) + 0 = 0         ⇒ K = λ
PR is perpendicular to line (ii)
∴ -1(-m + λ) + (m - λ) + 0 = 0
⇒ m = 0
Also line PQ is perpendicular to PR
⇒ 0 + 0 + (λ - 1)(λ + 1) = 0
⇒ λ = ±1
⇒ λ = 1 will be rejected as P will coincide with Q.

Create a free account to view solution

View Solution Free
Topic: Math miscellaneous·Practice all Math miscellaneous questions

More Math miscellaneous Questions

If a ∈ R and the equation -3(x - [x])2 + 2 (x - [x]) + a2 = 0 (where [x] denotes the greatest integer ≤ x) h...In the expansion of (1 + x + y + z)4 the ratio of coefficient of x2y, xy2z, xyz are:-...Coefficient of x9 in the expansion of is -...If makes an angle of π/3 with both and then can be...The integralis equal to :...