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Given three vectors a,b and c are non-ze...

Given three vectors a,b and c are non-zero and non-coplanar vectors. Then which of the following are coplanar.

A

`(|a|)/(|a|=2|b|)a+(|b|)/(|a|+|b|)b`

B

`|b|/(|a|+|b|)a+|a|/(|a|+|b|)b`

C

`(|a|)/(|a|+|b|)a+(|b|)/(|a|+2|b|)b`

D

`(|b|)/(2|a|+|b|)a+(|a|)/(2|a|+|b|)b`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Since, a and b are equally inclined to c, therefore c must be of the form `t((a)/(|a|)+(b)/(|b|))`
Now, `(|b|)/(|a|+|b|)a+(|a|)/(|a|+|b|)b=(|a||a|)/(|a|+|a|)((a)/(|a|)+(b)/(|b|))`
Also, `(|b|)/(2|a|+|b|)a+(|a|)/(2|a|+|b|)b=(|a||b|)/(2|a|+|b|)((a)/(|a|)+(b)/(|b|))`
Other two vectors cannot be written in the form `t((a)/(|a|)+(b)/(|b|))`.
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