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Question
The value of the expression `|vec"a" xx vec"b"|^2 + (vec"a".vec"b")^2` is ______.
Solution
The value of the expression `|vec"a" xx vec"b"|^2 + (vec"a".vec"b")^2` is `|vec"a"|^2 |vec"b"|^2`.
Explanation:
`|vec"a" xx vec"b"|^2 + (vec"a".vec"b")^2 = (|vec"a"||vec"b"| sin theta)^2 + (|vec"a"||vec"b"| cos theta)^2`
= `|vec"a"|^2 |vec"b"|^2 sin^2 theta + |vec"a"|^2 |vec"b"|^2 cos^2 theta`
= `|vec"a"|^2 |vec"b"|^2 * (sin^2theta + cos^2theta)`
= `|vec"a"|^2 |vec"b"|^2 * 1 = |vec"a"|^2 |vec"b"|^2`
Hence, the value of the filler is `|vec"a"|^2 |vec"b"|^2`.
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