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If the angle between the vectors veca an...

If the angle between the vectors `veca and vecb " is " pi/3` and the area of the triangle with adjacemnt sides parallel to `veca and vecb` is 3 , then a.b is

A

`sqrt3`

B

2sqrt3`

C

4sqrt3`

D

`sqrt3/2`

Text Solution

Verified by Experts

The correct Answer is:
B
we have,
` 1/2 |veca xx vecb|=3 `
` Rightarrow |veca xx vecb|=6 Rightarrow |veca||vecb|sin pi/ 3 =6 Rightarrow |veca||vecb| =4sqrt3`
` veca. Vecb = |veca||vecb| cos pi/ 3 = 4sqrt3 xx 1/2 =2sqrt3`
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