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Question: The plane 2x – 3y + 6z – 11 = 0 makes an angle sin<sup>–1</sup>(1) with the x-axis. Then the value o...

The plane 2x – 3y + 6z – 11 = 0 makes an angle sin–1(1) with the x-axis. Then the value of 'a' is :

A

32\frac{\sqrt{3}}{2}

B

23\frac{\sqrt{2}}{3}

C

37\frac{3}{7}

D

27\frac{2}{7}

Answer

27\frac{2}{7}

Explanation

Solution

Q DR's of the normal of the plane Ž 2, –3, 6

& DR's of x-axis is 1, 0, 0

& If 'q' is the angle between the plane

& x-axis, then sin q = 2(1)+(–3)(0)+(6)(0)22+(–3)2+621\frac{2(1) + (–3)(0) + (6)(0)}{\sqrt{2^{2} + (–3)^{2} + 6^{2}}\sqrt{1}}= 27\frac{2}{7}

Ž q = sin–1(27)\left( \frac{2}{7} \right)

\ a = 27\frac{2}{7}