If A=2i^ + 3j^+6k^ and B =3i^ -6j^+2k^ ,then vector perpendicular to both A and B has magnitude m times that of 6i^-2j^+3k^. Find m.

Let C  be the vector perpendicular to vector A and B, then C can be taken as the cross product of A and B. C=A×B=i^j^k^2363-62=i^3×2-6×-6+j^6×3-2×2+k^2×-6-3×3=42i^+14j^-21j^From the question422+142+-212=m62+-22+32762+22+32=m62+-22+32m=7

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