Question

The angle between the tangent plane to the sphere $x^{2} + y^{2} + z^{2} = 9$ at the point (2,1,2) and the XY - plane is}

• A. $\cos^{-1}(\frac{2}{3})$
• B. $\cos^{-1}(\frac{3}{\sqrt{5}})$
• C. $\cos^{-1}(\frac{4}{9})$
• D. $\cos^{-1}(\frac{\sqrt{2}}{3})$

Hint:

Normal of a sphere at $(x,y,z)$ is just the vector $(x,y,z)$. Normal of XY-plane is always the Z-axis vector ($0,0,1$).

Answer 1

The Correct Option is A