Find | a × b |, if a = i -3 j + 4 k and b = 4 i - j + 5 k .

We have, \(\vec{a}\)=  \(\hat{i}\) -3\(\hat{j}\)+ 4\(\hat{k}\) and \(\vec{b}\)=  4\(\hat{i}\) - \(\hat{j}\)+ 5\(\hat{k}\) .

\(\vec{a}\) ×\(\vec{b}\)= (-15 +4)\(\hat{i}\) -(5-16) \(\hat{j}\)+(-1+12) \(\hat{k}\)

\(\vec{a}\) ×\(\vec{b}\)  = (-11)\(\hat{i}\) + (11)\(\hat{j}\) + (11)\(\hat{k}\)

|\(\vec{a}\) ×\(\vec{b}\)|= √(-11)² +(11)² +(11)²

 |\(\vec{a}\) ×\(\vec{b}\)| = √363