Q.
If the foot of the perpendicular drawn from (1,9,7) to the line passing through the point (3,2,1) and parallel to the planes x+2y+z=0 and 3y−z=3 is (α,β,γ), then α+β+γ is equal to
Direction ratio of line =∣∣i^10j^23k^1−1∣∣ =i^(−5)−j^(−1)+k^(3) =−5i^+j^+3k^ M(−5λ+3,λ+2,3λ+1) PM⊥(−5i^+j^+3k^) −5(−5λ+2)+(λ−7)+3(3λ−6)=0 ⇒25λ+λ+9λ−10−7−18=0 ⇒λ=1
Point M=(−2,3,4)=(α,β,γ) α+β+γ=5