Angle between 2 Planes:

P1: 4x - 3y + z = -7, and P2: -3x + 2y - 4z = 5.

We can use the normal vectors here:

n₁ = 4i - 3j + k, and

n₂ = -3i +2j - 4k.

Test for parallel: n₁ and n₂ must be proportional and they are not.

Test for perpendicular: See of the dot product is zero:

n₁ · n₂ = 4*(-3) + (-3)*2 + 1*(-4) = -22 (not 0)

Hence the planes are not perpendicular either.

Now we find the angle between the normal vectors:

Hence, q = 143° , or 37° .