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Find the angle between the plane 2x + 3y...

Find the angle between the plane 2x + 3y - 5z = 10 and the line passing through the points (2,3,-1) and (1,2,1).

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The correct Answer is:
Hence, `theta = sin^(-1) ((15)/(sqrt(6) sqrt(38) ))`.
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(i) Find the angle between the line : (x + 1)/(2) = (y)/(3) = (z - 3)/(6) and the plane 10x + 12y - 11z = 3 (ii) Find the angle between the line : (x + 1)/(2) = (y -1)/(2) = (z -2)/(4) and the plane 2x + y - 3z + 4 =0 . (iii) Find the angle between the plane 2x + 4y - z = 8 and line (x - 1)/(2) = (2 - y)/(7) = (3z + 6)/(12) (iv) Find the angle between the line (x - 1)/(3) = (3 -y)/(-1) = (3z + 1)/(6) and the plane 3x - 5y + 2z = 10 .