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If |hata-hatb|= sqrt2 then calculate the...

If `|hata-hatb|= sqrt2` then calculate the value of `|hata+sqrt3hatb|`.

A

2

B

3

C

0.2

D

5

Text Solution

Verified by Experts

The correct Answer is:
A
Let `theta ` be the angle between `hata & hatb` then
`|hata- hatb| = sqrt(1^(2) + 1^(2)- 2(1) (1) cos theta)= sqrt2`
`rArr costheta = 0 rArr theta = 90^(@) or (pi)/(2) ` radian
`|hata+ sqrt3hatb| = sqrt(1+3+2sqrt3cos theta) = sqrt (1+3) = 2`
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