Question

How do you find the angle between the planes 2x+5y-z=6 and 3x-2y+6z=10?

Answer 1

The angle is `105.1º`

Explanation:

You look for the angle between the vectors normal to the planes:
Plane1, the vector is`〈2,5,-1〉`
Plane2, the vector is `〈3,-2,6〉`
The dot product is `〈2,5,-1〉.〈3,-2,6〉=6-10-6=-10`
The modulus of vector1 is `sqrt(4+25+1)=sqrt30`
The modulus of vector2 is `sqrt(9+4+36)=sqrt49=7`
The `costheta=-10/(7sqrt30)=-0.26`
`theta` is the angle between the planes
`:. theta=105.1º`