The plane 2x – 3y + 6z – 11 = 0 makes an angle sin–1($\alpha$) with x-axis. The value of $\alpha$ is equal to ______.

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The plane 2x – 3y + 6z – 11 = 0 makes an angle sin–1($\alpha$) with x-axis. The value of $\alpha$ is equal to $\frac{2}{7}$. Explanation: Direction ratios of the normal to the plane 2x – 3y + 6z – 11 = 0 are 2, – 3, 6 Direction ratios of x-axis are 1, 0, 0 $\therefore$ Angle between plane and line is `sin theta = (2(1) - 3(0) + 6(0))/(sqrt((2)^2 + (-3)^2 + (6^2))*sqrt((1)^2 + (0)^2 + (0)^2) = 2/sqrt(4 + 9 + 36) = $\frac{2}{7}$`

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