Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.

2x+y+3z-2=0 and x-2y+5=0

Open in App

Solution

Given planes are 2x +y +3z -2=0 and x-2y+0z+5=0

Here, $a_{1} = 2, b_{1} = 1, c_{1} = 3 a n d a_{2} = 1, b_{2} = - 2, c_{2} = 0$

$∴ a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 2 \times 1 + 1 \times (- 2) + 3 \times 0 = 0$

Thus, the given planes are perpendicular to each other.

Suggest Corrections

Similar questions

Q. In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.

2 x + y + 3 z - 2 = 0

and

x - 2 y + 5 = 0

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.

2x- 2y+ 4z+ 5= 0 and 3x- 3y+ 6z- 1= 0

Q. In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.

2 x - 2 y + 4 z + 5 = 0

and

3 x - 3 y + 6 z - 1 = 0

In the following exericise determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.

7x +5y +6z+ 30 =0 and 3x -y- 10z+ 4=0

2x+y+3z-2=0 and x-2y+5=0

2x- 2y+ 4z+ 5= 0 and 3x- 3y+ 6z- 1= 0

2x-y+3z-1=0 and 2x-y+3z+3=0

4x+8y+z-8=0 and y+z-4=0

In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.

(a)

(b)

(c)

(d)

(e)

Join BYJU'S Learning Program

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them. 2x+y+3z-2=0 and x-2y+5=0

Given planes are 2x +y +3z -2=0 and x-2y+0z+5=0 Here, a1=2,b1=1,c1=3 and a2=1,b2=−2,c2=0 ∴ a1a2+b1b2+c1c2=2×1+1×(−2)+3×0=0 Thus, the given planes are perpendicular to each other.

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.

2x+y+3z-2=0 and x-2y+5=0

Given planes are 2x +y +3z -2=0 and x-2y+0z+5=0

Here, $a_{1} = 2, b_{1} = 1, c_{1} = 3 a n d a_{2} = 1, b_{2} = - 2, c_{2} = 0$

$∴ a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 2 \times 1 + 1 \times (- 2) + 3 \times 0 = 0$

Thus, the given planes are perpendicular to each other.