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If |vec(a)|=2, |vec(b)|=5 and |vec(a)xxv...

If `|vec(a)|=2, |vec(b)|=5 and |vec(a)xxvec(b)| = 8`, then what is `vec(a). vec(b)` equal to ?

A

6

B

7

C

8

D

9

Text Solution

Verified by Experts

The correct Answer is:
A
Given `|a|=2, |b|=5 and |axxb|=8`
Also`|axxb|=|a|.|b|.|sin theta|`
`rArr |sin theta|=(8)/(2xx5)=(4)/(5)`
`rArr |cos theta|=(3)/(5) rArr cos theta = pm (3)/(5)`
`:. A.b = |a|.|b| cos theta = 2 xx 5 xx (3)/(5)=6`
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