Question

The coordinates of the point where the line (x + 1)/2 = (y + 2)/3 = (z + 3)/4  meets the plane x + y + 4z − 6 = 0 are

(A) (−1, −1, −1) 

(B) (1, −1, −1) 

(C) (−1, 1, −1) 

(D) (1, 1, 1)

Answer 1

Correct option is (D) (1,1,1)

Explanation :

P = (−1 + 2λ, −2 + 3λ, −3 + 4λ) is a point on the given line. Point P belongs to the given plane implies that

(-1 + 2λ) + (-2 + 3λ) + 4(-3 + 4λ) = 6

21λ = 21

λ = 1

Therefore, the required point is (−1 + 2, −2 + 3, −3 + 4) = (1, 1, 1).