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Let a, b, c be unit vectors such that a+...

Let a, b, c be unit vectors such that a+b+c=0. Which one of the following is correct?

A

` veca xx vecb = vecb xx vecc = vecc xx veca = vec0`

B

` veca xx vecb= vecb xx vecc = vecc xx veca ne vec0`

C

` veca xx vecb = vecb xx vecc = veca xx vecc= vec0`

D

` veca xx vecb, vecb xx vecc, vecc xx veca` are mutually perpendicular vectors.

Text Solution

Verified by Experts

The correct Answer is:
B
we have,
` veca + vecb + vecc = vec0`
` Rightarrow " Unit vectors " veca, vecb, vecc` respresent three sides of a triangle .
Triangle is equlateral.
Procesding as in illustration 15, we get
` veca xx vecb = vecb xx vecc = vecc xx veca`
Also, " ` 1/2 |veca xx vecb|=1/2 |vecb xx vecc| = 1/2 |vecc xx veca|` = Area of triangle
`Rightarrow 1/2|vecaxx vecb|=1/2|vecb xxvecc|=1/2 |veccxxveca|= sqrt3/4`
` veca xx vecb = vecb xx vecc = vecc xx veca ne vec0`
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