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.

Answer :

**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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If lines and intersect, then find the value of k and hence find the equation of the plane containing these lines.

Mathematics - Board PapersFind the coordinates of the point where the line through the points A(3, 4, 1) and B(5, 1, 6) crosses the XZ plane. Also find the angle which this line makes with the XZ plane.

Mathematics - Board PapersState True or False for the statements

The angle between the lineand the plane is .

Mathematics - ExemplarThe sine of the angle between the straight lineand the plane 2x – 2y + z = 5 is

Mathematics - ExemplarThe plane 2x – 3y + 6z – 11 = 0 makes an angle sin^{–1}(α) with x-axis. The valueof α is equal to

Mark against the correct answer in each of the following:

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RS Aggarwal - Mathematics

Mark against the correct answer in each of the following:

The angle between the line and the plane is

RS Aggarwal - Mathematics