Try this solution:
1. Given: α:4x-y+2z=-4 and β:x+y-4z=3.
if vector n₁⊥α and n₂⊥β, then required cosine is:
[tex] cos \gamma =|\frac{n_1*n_2}{|n_1|*|n_2|}|; [/tex]
where n₁*n₂=4*1+(-1)*1+2*(-4) and |n₁|*|n₂|=√(4²+1²+2²)*√(1²+1²+4²).
2. Using the formula of cosine:
[tex] cos \gamma=|\frac{4-1-8}{\sqrt{21}*\sqrt{18}}|=\frac{5}{3\sqrt{42}}=0.2572 [/tex]
answer: ≈0.2572
