Home
Class 12
MATHS
The vectors vecx and vecy satisfy the eq...

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`

Text Solution

Verified by Experts

The correct Answer is:
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`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

  • ELLIPSE

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

Four vectors veca, vecb, vecc and vecx satisfy the relation (veca.vecx)vecb=vecc+vecx where vecb.veca ne 1 . The value of vecx in terms of veca, vecb and vecc is equal to

Let veca=hati-hatj,vecb=hati+hatj+hatk and vecc be a vector such that vecaxxvecc+vecb=vec0 and veca.vecc=4 , then |vecc|^(2) is equal to:

If veca=hatj-hatk and vecc=hati+hatj+hatk are given vectors, and vecb is such that veca.vecb=3 and vecaxxvecb+vecc=0 than |vecb|^(2) is equal to ………………

The scalars l and m such that lveca + m vecb =vecc, " where " veca, vecb and vecc are given vectors, are equal to

The scalars l and m such that lveca + m vecb =vecc, " where " veca, vecb and vecc are given vectors, are equal to

Solve for vec x,vecx xx vec b=veca , where veca,vecb are two given vectors such that veca is perpendicular to vecb .

Write the unit vector in the direction of vecA=5veci+vecj-2veck .

Given two orthogonal vectors vecA and VecB each of length unity. Let vecP be the vector satisfying the equation vecP xxvecB=vecA-vecP . then vecP is equal to

Given two orthogonal vectors vecA and vecB each of length unity. Let vecP be the vector satisfying the equation vecP xxvecB=vecA-vecP . then vecP is equal to