Find the angle between planes $2 x + 2 y - 3 z - 5 = 0$ and
$3 x - 3 y + 5 z - 3 = 0$ .

Open in App

Solution

We have,
$\begin{matrix} π_{1} : 2 x + 2 y - 3 z = 5 π_{2} : 3 x - 3 y + 5 z = 3 \end{matrix}$
$cos 0 = \frac{| 6 - 6 - 15 |}{\sqrt{9 + 4 + 4} \sqrt{9 + 9 + 25}}$
$cos 0 = \frac{15}{\sqrt{17} \sqrt{43}}$
$θ = {cos}^{- 1} (\frac{15}{\sqrt{17} \sqrt{43}})$
Then,
We get $θ = {cos}^{- 1} (\frac{15}{\sqrt{17} \sqrt{43}})$

Suggest Corrections

Similar questions

Q. Angle between the planes

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

and

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

{cos}^{- 1} \frac{k}{\sqrt{17} \sqrt{43}}

then

k

Q. Find the angle between the planes x+2y+2z-5=0 and 3x+3y+2z-8=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)

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

Q. Solve the equations

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

Find xyz?

Join BYJU'S Learning Program

Find the angle between planes 2x+2y−3z−5=0 and 3x−3y+5z−3=0.

We have,π1:2x+2y−3z=5π2:3x−3y+5z=3cos0=|6−6−15|√9+4+4√9+9+25cos0=15√17√43θ=cos−1(15√17√43)Then,We get θ=cos−1(15√17√43)

Find the angle between planes $2 x + 2 y - 3 z - 5 = 0$ and
$3 x - 3 y + 5 z - 3 = 0$ .