Question

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 $x+2 y+z=0$ and $3 y-z=3$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to

• A. $-1$
• B. 1
• C. 3
• D. 5

Answer 1

Answer: (D)

5

Answer 2

The correct answer is (D) : 5

Direction ratio of line =∣∣​i^10​j^​23​k^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