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If the magnitude of sum of two vectors i...

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vector, the angle between these Vector is

A

`90^(@)`

B

`45^(@)`

C

`180^(@)`

D

`0^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) suppose two vector sr eP and Q . It is given that
`|P+Q|=|P-Q|`
Let angle between PandQ is `phi`
`therefore P^(2)+Q^(2) +2PQ cosphi=P^(2)+Q^(2)-2PQcosphi`
`implies4PQcosphi=0`
`implies cosphi=0 [thereforeP,Qne0]`
`=.phi=(pi)/(2) =90^(@)`
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Knowledge Check

  • If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

    A
    `45^(@)`
    B
    `180^(@)`
    C
    `0^(@)`
    D
    `90^(@)`

  • If the magnitude of sum of two vectors is equal to the magnitude of difference of the two voctors, the angle between these vectors is :

    A
    `1^(@)`
    B
    `90^(@)`
    C
    `45^(@)`
    D
    `180^(@)`

  • There are two vectors of equal magnitudes. When these vectors are added, then magnitude of the resultant is also equal to the magnitude of each of the two given vectors. Angle between the vectors is

    A
    `120^(@)`
    B
    `60^(@)`
    C
    `30^(@)`
    D
    `150^(@)`

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