Question

If the intercept form of the equation of the plane 2x − 3y + 4z = 12 is `x/a + y/b + z/c = 1,` then the values of a, b, c are respectively,

Options

• a = 6, b = −4, c = 3

• a = − 6, b = −4, c = 3

• a = 6, b = 4, c = 3

• a = 6, b = 4, c = −3

Answer 1

a = 6, b = −4, c = 3

Explanation:

Given that,

If the intercept form of the equation of the plane ax - by + cz = d is 

`x/a + y/b + z/c = 1`

we have, 2x − 3y + 4z = 12

On dividing by 12 on both side,

`(2x)/12 − (3y)/12 + (4z)/12 = 12/12`

`x/6 − y/4 + z/3 = 1`

On comparing with the equation. (i)

a = 6, b = − 4, c = 3

∴ Option a = 6, b = −4, c = 3 is correct.