Cosine of the Angle between Planes:

P1: -x + 4y - 2z = 8, and P2: 3x - y + 4z = -5.

We can find the cosine between the normal vectors, which we can obtain from the coefficients in the equations of the planes:

n₁ = -i + 4j - 2k, and

n₂ = 3i - j + 4k.

Now we determine the cosine: