Question

If A= 2i + 3j + 7k and B= i + 4j + 5k , find A×B . Show that A×B = (B×A)​

Answer 1

Answer:

Given,A=2i+3j+7k. & B=i+4j+5k

So,A×B={2i+3j+7k}×{i+4j+5k}

=(2i)(i+4j+5k)+3j(i+4j+5k)+7k(i+4j+5k)

=8(ij)+10(ik)+3(ji)+15(jk)+7(ki)+28(kj)

=8k-10j-3k+15i+7j-28i

=5k-3j-13i

= -13i-3j+5k.

L.H.S,A×B= -13i-3j+5k

R.H.S,।B×A।=(i+4j+5k)×(2i+3j+7k)

=3(ij)+7(ik)+8(ji)+28(jk)+10(ki)+15(kj)

=3k-7j-8k+28i+10j-15i

= । 13i+3j-5k।

= -13i-3j+5k.

Hence,L.H.S=R.H.S