Q. 6

Find the angle between the line joining the points A(3, - 4, - 2) and B(12, 2, 0) and the plane 3x – y + z = 1.

Given - A = (3, - 4, - 2) , B = (12, 2, 0) and 3x - y + z = 1

To find – The angle between the line joining the points A and B and the plane

Tip – If P = (a, b, c) and Q = (a’, b’, c’), then the direction ratios of the line PQ is given by ((a’ - a), (b’ - b), (c’ - c))

The direction ratios of the line AB can be given by

((12 - 3), (2 + 4), (0 + 2))

= (9, 6, 2)

Direction ratios of the normal of the plane = (3, - 1, 1)

Formula to be used – If (a, b, c) be the direction ratios of a line and (a’, b’, c’) be the direction ratios of the normal to the plane, then, the angle between the two is given by

The angle between the line and the plane

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