Which of the following planes is equally inclined to the planes 4x+3y -5z =0 and 5x -12y+13z =0?

a. 11x -3y =0

b. 3x +11y =0

c. 3x +11y =65z

d. none of these

Question

Which of the following planes is equally inclined to the planes
4x+3y -5z =0 and 5x -12y+13z =0?
a 11x -3y =0
b 3x +11y =0
c 3x +11y =65z
d none of these

Duke Biswass · Accepted Answer

If $A_{1} x + B_{1} y + C_{1} z + D_{1} = 0$ and $A_{2} x + B_{2} y + C_{2} y + D_{2} = 0$ are the plane equations, then the angle between the planes is given by

$\cos α = \frac{| A_{1} A_{2} + B_{1} B_{2} + C_{1} C_{2} |}{{({A_{1}}^{2} + {B_{1}}^{2} + {C_{1}}^{2})}^{\frac{1}{2}} {({A_{2}}^{2} + {B_{2}}^{2} + {C_{2}}^{2})}^{\frac{1}{2}}}$

In option a) 11x - 3y = 0

with 4x+3y-5z = 0

$\cos α = \frac{7 \sqrt{65}}{130}$

with the plane 5x-12y+13z = 0

$\cos α = \frac{7 \sqrt{65}}{130}$

SO the correct answer is a) 11x - 3y = 0

Which of the following planes is equally inclined to the planes 4x+3y -5z =0 and 5x -12y+13z =0? a. 11x -3y =0 b. 3x +11y =0 c. 3x +11y =65z d. none of these

Which of the following planes is equally inclined to the planes 4x+3y -5z =0 and 5x -12y+13z =0?

a. 11x -3y =0

b. 3x +11y =0

c. 3x +11y =65z

d. none of these