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The sum and diffrence of two perpendicul...

The sum and diffrence of two perpendicular vector of equal length are

A

Perpendicular to each other and of equal length.

B

Perpendicular to each other and of different length

C

Of equal length and have an obtuse angle between them

D

Of equal length and have an acute angle between them

Text Solution

Verified by Experts

The correct Answer is:
A
Given `|vec(A)|=|vec(B)|` or `A=B`
Sum `vec(R )=vec(A)+vec(B) rArr |vec(R )|=sqrt(A^(2)+B^(2))=sqrt(2A)`
Difference `vec(S)=vec(A)-vec(B) rArr |vec(S)|=sqrt(A^(2)+B^(2))=sqrt(2A)`
`alpha_(1)=45^(@), alpha_(2)=45^(@)`
Hence, `vec(R )` and `vec(S)` will be perpendicular and also of equal lengths.
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Knowledge Check

  • Dot product of two mutual perpendicular vector is

    A
    0
    B
    1
    C
    `oo`
    D
    None of these

  • veca and vecb are two given vectors. On these vectors as adjacent sides a parallelogram is constructed. The vector which is the altitude of the parallelogam and which is perpendicular to veca is not equal to

    A
    `{((veca.vecb))/(|veca|^(2))}veca-vecb`
    B
    `1/(|veca|^(2)){(veca.vecb)veca-(veca.veca)vecb}`
    C
    `(vecaxx(vecaxxvecb))/(|veca|^(2))`
    D
    `(vecaxx(vecbxxveca))/(|vecb|^(2))`

  • The vector sum of two forces is perpendicular to their vector differences. In that cases, the forces

    A
    are not equal to each other In magnitude
    B
    are parallel
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    D
    are equal to each other In magnitude
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