Question

The vectors `vecx` and `vecy` satisfy the equation `pvecx+qvecy=veca` (where p,q are scalar constants and `veca` is a known vector). It is given that `vecx.vecy ge (|veca|^(2))/(4pq)`, then `(|vecx|)/(|vecy|)` is equal to `(pq gt 0)`
A. 1
B. `p^(2)/q^(2)`
C. `p/q`
D. `q/p`

Answer 1

Correct Answer - D
`pvecx+qvecy=veca`
`|pvecx-qvecy|^(2)= |pvecx+qvecy|^(2)-4pqvecx.vecy ge0`
but `vecx.vecyge(|veca|^(2))/(4pq)`
`rArr |veca|^(2)=4pqvecx.vecy`
`rArr |pvecx-qvecy|=0`
`rArr pvecx=qvecy rArr vecx=veca/(2p), vecy=veca/(2q)`
`rArr |vecx|/|vecy|=q/p`