If `vecr and vecs` are non-zero constant vectors and the scalar b is chosen such that `|vecr+bvecs|` is minimum, then the value of `|bvecs|^(2)+|vecr+bvecs|^(2)` is equal to

Options

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

Answer

b

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) `