Question

The angle between the line $\frac{x}{2} = \frac{y}{3} = \frac{z}{4}$ and the plane $3x + 2y - 3z = 4$is

• A. $45{^\circ}$
• B. $0{^\circ}$
• C. $\cos^{- 1}\left( \frac{24}{\sqrt{29}\sqrt{22}} \right)$
• D. $90{^\circ}$

Answer 1

Answer: (B)

$0{^\circ}$

Answer 2

Angle between the plane and line is

$\sin \theta = \frac { a a ^ { \prime } + b b ^ { \prime } + c c ^ { \prime } } { \sqrt { a ^ { 2 } + b ^ { 2 } + c ^ { 2 } } \sqrt { a ^ { \prime 2 } + b ^ { \prime 2 } + c ^ { \prime 2 } } }$

Here, $a a ^ { \prime } + b b ^ { \prime } + c c ^ { \prime } = 2 \times 3 + 3 \times 2 - 4 \times 3 = 0$

$\therefore \sin \theta = 0$ ⇒