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Question
If `|vec"a" xx vec"b"|^2 + |vec"a".vec"b"|^2` = 144 and `|vec"a"|` = 4, then `|vec"b"|` is equal to ______.
Solution
If `|vec"a" xx vec"b"|^2 + |vec"a".vec"b"|^2` = 144 and `|vec"a"|` = 4, then `|vec"b"|` is equal to 3.
Explanation:
`|vec"a" xx vec"b"|^2 + |vec"a".vec"b"|^2` = 144
⇒ `(|vec"a"||vec"b"|| sin theta)^2 + (|vec"a"||vec"b"| cos theta)^2` = 144
⇒ `|vec"a"|^2 |vec"b"|^2 sin^2theta + |vec"a"|^2 |vec"b"|^2 cos^2theta` = 144
⇒ `|vec"a"|^2 |vec"b"|^2 (sin^2theta + cos^2theta)` = 144
⇒ `|vec"a"|^2 |vec"b"|^2` = 12
⇒ `4 * |vec"b"|` = 12
⇒ `|vec"b"|` = 3
Hence, the value of the filler is 3.
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