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Let p bari+3barj+4bark and sqrt(q)bari+5...

Let `p bari+3barj+4bark and sqrt(q)bari+5bark` be two vectors where `p, q ge 0` are two scalars. If (p, q) is a pair of values for which their lengths are equal, then there can be

A

Infinitely many such pairs exist

B

Finite such pairs exist

C

No pair exist

D

Can not be determind

Text Solution

Verified by Experts

The correct Answer is:
A
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Knowledge Check

  • Let bara=barj-bark and barc= bari -barj-bark . Then the vector barb satisfying bara xx barb + barc = 0 and bara. barb =3 is

    A
    `-bari+barj-2bark`
    B
    `2bari-barj+2bark`
    C
    `bari-barj-2bark`
    D
    `bari+barj-2bark`

  • Let a=2bari + barj-bark and barb = barI +3bark . If barc is a unit vectors such that [bara barb barc] is maximum, then barc is

    A
    `1/(sqrt14)(3bari+barj+2bark)`
    B
    `1/(sqrt6)(2bari+barj-bark)`
    C
    `1/(sqrt10)(bari+3bark)`
    D
    `1/(sqrt(59))(3bari-7barj-bark)`

  • Let bara = bari + 2 barj - bark, and bar b = bari + barj + bark. If barp is a unit vector such that [ bar a barb barp] is maximum, then bar p=

    A
    `(1)/(sqrt6) (bari - 2 barj + bark)`
    B
    `(1)/(sqrt3) (bari + barj - bark)`
    C
    `(1)/(sqrt14) (3 bari - 2 barj - bark)`
    D
    `(1)/(sqrt14) (bar I + 2 barj + 3 bark )`

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