Let L 1 : 3 x − 1 = − 1 y − 1 = 0 z + 1 and L 2 : 2 x − 2 = 0 y = α z + 4 , α ∈ R , be two lines, which intersect at the point B . If P is the foot of perpendicular from the point A (

Question

Let L 1 ​ : 3 x − 1 ​ = − 1 y − 1 ​ = 0 z + 1 ​ and L 2 ​ : 2 x − 2 ​ = 0 y ​ = α z + 4 ​ , α ∈ R , be two lines, which intersect at the point B . If P is the foot of perpendicular from the point A ( 1 , 1 , − 1 ) on L 2 ​ , then the value of 26 α ( PB ) 2 is _________

TestHub · Accepted Answer

Point B ​ ( 3 λ + 1 , − λ + 1 , − 1 ) ≡ ( 2 μ + 2 , 0 , αμ − 4 ) 3 λ + 1 = 2 μ + 2 − λ + 1 = 0 − 1 = αμ − 4 λ = 1 , μ = 1 , α = 3 B ( 4 , 0 , − 1 ) ​ Let Point ’ P ’ is ( 2 δ + 2 , 0 , 3 δ − 4 ) Dr’s of AP < 2 δ + 1 , − 1 , 3 δ − 3 > A P ⊥ L 2 ​ ⇒ δ = 13 7 ​ P ( 13 40 ​ , 0 , 13 − 31 ​ ) ∴ 26 α ( PB ) 2 = 26 × 3 × ( 169 144 ​ + 169 324 ​ ) = 216

Mathematics - Vector Question with Solution | TestHub

Doubts & Discussion