The angle between the line x + 1/1 = y/2 = z - 1/1 and a normal to the plane x – y + z = 0 is ​

Question

The angle between the line \(\frac{x+1}1\) = \(\frac{y}2\) = \(\frac{z-1}1\) and a normal to the plane x – y + z = 0 is 

A. 0° 

B. 30° 

C. 45° 

D. 90°

Answer 1

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

Equation of plane is x – y + z = 0 

To find: Angle between a line and the normal to a plane. 

Formula Used: If θ is the angle between two lines with direction ratios b₁:b₂:b₃ and c₁:c₂:c₃, then

Explanation: 

Direction ratios of given line is 1 : 2 : 1 

Direction ratios of the normal to the plane is 1 : -1 : 1 

Therefore,

cos θ = 0 

θ = 90° 

Therefore angle between them is 90°