Q. 12

# Mark against the correct answer in each of the following:The line meets the plane 2x + 3y – z = 14 in the pointA. (2, 5, 7)B. (3, 5, 7)C. (5, 7, 3)D. (6, 5, 3)

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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Find the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

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