Question

The equation of plane which is passing through (2, 1, 3) and having equal X and Y-intercept and Z-intercept 14 is ____

(A) 11x – 11y + 3z = 42

(B) 11x + 11y + 3z = 42

(C) 11x + 11y – 3z = 42

(D) 11x + 11y + 3z + 42 = 0   

Answer 1

The correct option (B) 11x + 11y + 3z = 42  

Explanation:

given: X-intercept = Y-intercept = a

Z-intercept = 14 

 ∴ (x/a) + (y/a) + (z/14) = 1 ......(1)

point (2, 1, 3) is on the plane

∴ (2/a) + (1/a) + (3/14) = 1

⇒ (3/a) = (11/14)

∴ a = (42/11) 

⇒ equation is (11/42)x + (11/42)y + (z/14) = 1

∴ 11x + 11y + 3z = 42.