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If non-zero vectors a annd b are equally...

If non-zero vectors a annd b are equally inclined to coplanar vector c, then c can be

A

`(|veca|)/(|veca|+2|vecb|)veca + (|vecb|)/(|veca| + |vecb|) vecb`

B

`(|vecb|)/(|veca| + |vecb|) veca + (|veca|)/(|veca|+ |vecb|) vecb`

C

`(|veca|)/(|veca|+2|vecb|)veca + (|vecb|)/(|veca|+ 2|vecb|)vecb`

D

`(|vecb|)/(2|veca| + |vecb|) veca + (|veca|)/(2|veca|+ |vecb|) vecb`

Text Solution

Verified by Experts

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