If the plane 2x – y + z = 0 is parallel to the line 2x - 1/2 = 2 - /2 = z + 1/a, then the value of a is ​

Question

If the plane 2x – y + z = 0 is parallel to the line \(\frac{2x-1}2\) = \(\frac{2-y}2\) = \(\frac{z+1}a\), then the value of a is 

A. -4 

B. -2 

C. 4 

D. 2

Answer 1

Given: Plane 2x – y + z = 0 is parallel to the line

\(\frac{2x-1}2\) = \(\frac{2-y}2\) = \(\frac{z+1}a\)

To find: value of a 

Formula Used: If two lines with direction ratios a₁:a₂:a₃ and b₁:b₂:b₃ are perpendicular, then 

a₁b₁ + a₂b₂ + a₃b₃ = 0 

Explanation: 

Since the plane is parallel to the line, the normal to the plane will be perpendicular to the line. 

Equation of the line can be rewritten as

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

Direction ratio of line is 1 : -2 : a 

Therefore, 

2 + 2 + a = 0 

a = -4 

Therefore, a = -4