Find a vector of magnitude 6,which is perpendicular to both the vectors 2i^-j^+2k^ and 4i^-j^+3k^ Pls provide me detailed solution - Maths - Vector Algebra

Question

Find a vector of magnitude 6,which is perpendicular to both the
vectors 2i^-j^+2k^ and 4i^-j^+3k^ Pls provide me detailed solution
as my ans is not matching with the given ans

Manbar Singh · Accepted Answer

Let a→ = 2i^ - j^ + 2k^  and  b→ = 4i^ - j^ + 3k^A unit vector ⊥ to both a→ and b→ = a→ × b→a→ × b→Now,a→ × b→ = i^j^k^2-124-13 = i^-3+2-j^6-8+k^-2+4 = -i^ + 2j^ + 2k^a→ × b→ = -12+22+22 = 9 = 3So, A unit vector ⊥ to both a→ and b→ = a→ × b→a→ × b→= -i^ + 2j^ + 2k^3Now, required vector of magnitude 6 =  6-i^ + 2j^ + 2k^3 = 2-i^ + 2j^ + 2k^ = -2i^ + 4j^ + 4k^

Find a vector of magnitude 6,which is perpendicular to both the vectors 2i^-j^+2k^ and 4i^-j^+3k^.Pls provide me detailed solution as my ans is not matching with the given ans.