Question

The equation of a plane passing through the point A(2, -3, 7) and making equal intercepts on the axes, is 

A. x + y + z = 3 

B. x + y + z = 6 

C. x + y + z = 9 

D. x + y + z = 4

Answer 1

Given: A(2, -3, 7) is a point on the plane making equal intercepts on the axes. 

Formula Used: Equation of plane is x/a + y/b + z/c = 1 where (x, y, z) is a point on the plane and a, b, c are intercepts on x-axis, y-axis and z-axis respectively. 

Explanation: 

Let the equation of the plane be

x/a + y/b + z/c = 1...(1)

Here a = b = c = p (let’s say) 

Since (2, -3, 7) is a point on the plane, 

(1) becomes

\(\frac{2-3+7}p\) = 1

p = 6 

Therefore equation of the plane is 

x + y + z = 6