Q. 17

# Mark against the correct answer in each of the following:

The angle between the line and a normal to the plane x – y + z = 0 is

A. 0°

B. 30°

C. 45°

D. 90°

Answer :

Given: Equation of line is

_{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 b_{1}:b_{2}:b_{3} and c_{1}:c_{2}:c_{3}, 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°

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RS Aggarwal - Mathematics