Statement 1: If $\theta$ denotes the angle between the line $(x-2)/2=(y-1)/(-3)=(z+2)/(-2)$ and the plane $x+y-z=5$, then $\theta=\sin^{-1}(1/\sqrt{51})$. Statement 2: The angle made by a line with a plane is the complementary angle of the angle between that line and the normal to

Question

Statement 1: If $\theta$ denotes the angle between the line $(x-2)/2=(y-1)/(-3)=(z+2)/(-2)$ and the plane $x+y-z=5$, then $\theta=\sin^{-1}(1/\sqrt{51})$. Statement 2: The angle made by a line with a plane is the complementary angle of the angle between that line and the normal to the plane.

Accepted Answer

Statement 1 is false, Statement 2 is true. Statement 1 is incorrect because the calculation of the angle between the line and the plane does not yield the given value, while Statement 2 is accurate as it correctly describes the relationship between the angle of a line with a plane and the angle with the plane's normal.

Statement 1: If \(\theta\) denotes the angle between the line \((x-2)/2=(y-1)/(-3)=(z+2)/(-2)\) and the plane \(x+y-z=5\), then \(\theta=\sin^{-1}(1/\sqrt{51})\). Statement 2: The angle made by a line with a plane is the complementary angle of the angle between that line and the normal to the plane.

Solution

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