Determine the unit vector parallel to the cross product of the vectors →A = −3^i + 5^j + 10^k and →B = −6^i + 5^j + 2^k
The unit vector parallel to (→A×→B) is given by ^n =→A×→B→|A×→B|
So, let us first determine →A×→B
Now,→A×→B =(−3^i+5^j+10^k)×(−6^i+5^j+2^k)=∣∣
∣
∣∣^i^j^k3−510652∣∣
∣
∣∣=^i(−10−50)=60^i+54^j+45^k
Magnitude:|→A×→B|=√(−60)2+(54)2+(45)2=√8541
So required unit vector:^n −60^i+54^j+45^k√8541