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If veca and vecb are unit vectors, the...

If ` veca and vecb` are unit vectors, then the greatest value of `|veca +vecb|+ |veca -vecb|` is

A

2

B

4

C

`2sqrt2`

D

`sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
C
Let ` theta` the angle between unit vectors ` veca and vecb` .
Then , `veca.vecb = cos theta`
Now,
` |veca +vecb|^(2) `
` = |veca|^(2) =|veca|^(2) + 2veca.vecb = 2 + 2cos theta = 4 cos theta = 4 cos^(2) " " theta/2`
and ,
` |veca -vecb|^(2) `
` |veca|^(2) +|vecb|^(2) -2 (veca .vecb) =2 -2 cos theta = 4 cos^(2) "" theta/2`
` Rightarrow |veca +vecb| = 2cos "" theta/2 ,|veca -vecb|=2 sin "" theta/2`
` Rightarrow |veca +vecb|+|veca-vecb| =2 (cos ""theta/2 = sin "" theta/2) le 2sqrrt2`
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