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`

Options

A. `2|vecr|^(2)`
B. `|vecr|^(2)//2`
C. `3|vecr|^(2)`
D. `|vecr|^(2)`

Answer

d

Explanation

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) `