Q. 23

Mark against the A. x + y – 3z = 2

B. y + 4z = 7

C. y + 3z = 6

D. x + 5y – 3z = 4

Answer :

Given: Plane passes through the points A(2, 3, 1) and B(4, -5, 3) and is parallel to x-axis


To find: Equation of plane


Formula Used: Equation of a plane parallel o x-axis is


b(y – y1) + c(z – z1) = 0


Explanation:


Let the equation of the plane be


b(y – y1) + c(z – z1) = 0


Since A(2, 3, 1) lies on the plane,


b(y – 3) + c(z – 1) = 0 … (1)


Since B(4, -5, 3) lies on the plane,


b(-5 – 3) + c(3 – 1) = 0


-8b + 2c = 0 or –4b + c = 0


b : c = 1 : 4


Substituting in (1),


y – 3 + 4z – 4 = 0


y + 4z = 7


The equation of the plane is y + 4z = 7

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