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