The angle between the line x - 2/1 = y + 3/-2 = z + 4/-3 and the plane 2x – 3y + z = 5 is ​

Question

The angle between the line \(\frac{x-2}1\) = \(\frac{y+3}{-2}\) = \(\frac{z+4}{-3}\) and the plane 2x – 3y + z = 5 is

A. cos-1\((\frac{5}{14})\)

B. cos-1\((\frac{5}{14})\)

C. cos-1\((\frac{5}{14})\) 

D. cos-1\((\frac{5}{14})\)

Answer 1

Given: Equation of line is \(\frac{x-2}1\) = \(\frac{y+3}{-2}\) = \(\frac{z+4}{-3}\) 

Equation of the plane is 2x – 3y + z = 5 

To find: angle between line and plane 

Formula Used: If θ is the angle between a line with direction ratio b₁:b₂:b₃ and a plane with direction ratio of normal n₁:n₂:n₃, then

Explanation: 

Here direction ratio of the line is 1 : -2 : -3 

Direction ratio of normal to the plane is 2 : -3 : 1 

Therefore,

Therefore, angle between the line and plane is sin^-1 \(\frac{5}{14}\)