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If vec ra n d vec s are non-zero consta...

If ` vec ra n d vec s` are non-zero constant vectors and the scalar `b` is chosen such that `| vec r+b vec s|` is minimum, then the value of `|b vec s|^2+| vec r+b vec s|^2` is equal to `2| vec r|^2` b. `| vec r|^2//2` c. `3| vec r""|^2` d. `|r|^2`

A

`2|vecr|^(2)`

B

`|vecr|^(2)//2`

C

`3|vecr|^(2)`

D

`|vecr|^(2)`

Text Solution

Verified by Experts

The correct Answer is:
b
For minimum value `|vecr+ bvecs|=0`
Let `vecr and vecs` are anti - parallel so `bvecs =- vecr`
`|bvecs|^(2) + |vecr + bvecs|^(2) = |-vecr|^(2) + |vecr-vecr|^(2) = |vecr|^(2) `
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