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Question
If `|vec"a"|` = 10, `|vec"b"|` = 2 and `vec"a".vec"b"` = 12, then value of `|vec"a" xx vec"b"|` is ______.
Options
5
10
14
16
Solution
If `|vec"a"|` = 10, `|vec"b"|` = 2 and `vec"a".vec"b"` = 12, then value of `|vec"a" xx vec"b"|` is 16.
Explanation:
Given that `|vec"a"|` = 10, `|vec"b"|` = 2 and `vec"a".vec"b"` = 12
∴ `vec"a" . vec"b" = |vec"a"||vec"b"| cos theta`
⇒ 12 = `10 * 2 * cos theta`
⇒ `cos theta = 12/20 = 3/5`
∴ `sin theta = sqrt(1 - cos^2theta)`
⇒ `sin theta = sqrt(1 - (3/5)^2`
⇒ `sin theta = sqrt(1 - 9/25)`
⇒ `sin theta = sqrt(16/25)`
⇒ `sin theta = 4/5`
Now `|vec"a" xx vec"b"| = |vec"a"| |vec"b"| sin theta`
= `10 * 2 * 4/5`
= 16
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