Q. 12

Mark against the correct answer in each of the following:

The line meets the plane 2x + 3y – z = 14 in the point

A. (2, 5, 7)

B. (3, 5, 7)

C. (5, 7, 3)

D. (6, 5, 3)

Answer :

Given: Line meets plane 2x + 3y – z = 14


To find: Point of intersection of line and plane.


Explanation:


Let the equation of the line be



Therefore, any point on the line is (2λ + 1, 4λ +2, -3λ +3)


Since this point also lies on the plane,


2(2λ + 1) + 3(4λ +2) – (-3λ +3) =14


4λ + 2 + 12λ + 6 + 3λ – 3 = 14


19λ + 5 = 14



Therefore the required point is (3, 5, 7).

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