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If veca, vecb,vecc are unit vectors such...

If `veca, vecb,vecc` are unit vectors such that `veca` is perpendicular to the plane of `vecb, vecc` and the angle between `vecb,vecc` is `pi/3`, then `|veca+vecb+vecc|=`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `|veca|=1,|vecb|=1, |vecc|=1`
`veca.vecb=0` and `veca.vecc=0`
Also, `vecb.vecc=|vecb|.|vecc|cospi/3=1.1.1/2=1/2`
Now, `|veca+vecb+vecc|^(2)`
`=veca^(2)+vecb^(2)+vecc^(2)+2veca.vecb+2vecb.vecc`
`rArr 1^(2)+1^(2)+1^(2)+2.1/2=4`
`therefore |veca+vecb+vecc|=2`
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