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 \(\frac{5}{14}\)