Find a unit vector perpendicular to A=2i^+3j^+k^ and B=i^-j^+k^ both.

As we have read, C=A×B is a vector perpendicular to both A and B. Hence, a unit vector n^ perpendicular to A and B can be written asn^=CC=A×B|A×B|Here, A×B=i^j^k^2311-11=i^(3+1)+j^(1-2)+k^(-2-3)=4i^-j^-5k^Further,|A×B|=(4)2+(-1)2+(-5)2=42The desired unit vector isn^=A×B|A×B|n^=142(4i^-j^-5k^)