Angle between a Plane and a Line

Q.

The angle between the line $r=\left(i+2j+3k\right)+\lambda \left(2i+3j+4k\right)$and the plane $r$ . $\left(i+2j-2k\right)=0$ is

1. $0°$

2. $60°$

3. $30°$

4. $90°$

5. $45°$

Q. If angle between line and plane is $\theta$ then the angle between line and the normal to plane is $\frac{\pi }{2}-\theta$

1. True
2. False

Q. The plane which bisects the line segment joining the points $(-3,-3,4)$ and $(3,7,6)$ at right angles, passes through which one of the following points?

1. $(4,-1,7)$
2. $(4,1,-2)$
3. $(2,1,3)$
4. $(-2,3,5)$

Q. The three planes 4y + 6z = 5; 2x + 3y + 5z = 5; 6x + 5y + 9z = 10.

1. meet in a point
2. have a line in common
3. form a triangular prism
4. mutuvally perpendicular

Q. If an angle between the line, $\frac{x+1}{2}=\frac{y-2}{1}=\frac{z-3}{-2}$ and the plane, $x-2y-kz=3$ is ${\cos }^{-1}\left(\frac{2\sqrt{2}}{3}\right)$, then a value of $k$ is :

1. $\sqrt{\frac{5}{3}}$
2. $\sqrt{\frac{3}{5}}$
3. $-\frac{3}{5}$
4. $-\frac{5}{3}$