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The sum and difference of two vectors ar...

The sum and difference of two vectors are perpendicular to each other. Prove that the vectors are equal in magnitude.

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To prove that two vectors \( \vec{A} \) and \( \vec{B} \) are equal in magnitude given that their sum and difference are perpendicular, we can follow these steps: ### Step 1: Define the vectors Let the two vectors be \( \vec{A} \) and \( \vec{B} \). ### Step 2: Write the expressions for the sum and difference The sum of the vectors is given by: \[ ...
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Knowledge Check

  • 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

  • Two vectors vecP and vecQ that are perpendicular to each other are :

    A
    `vecP = 3hati +3hatj + 2hatk, vecQ = 2hati - 2hatj + 2hatk`
    B
    `vecP = 2hati +3hatj + 2hatk, vecQ = 2hati - 2hatj + 2hatk`
    C
    `vecP = 2hati -3hatj + 2hatk, vecQ = 2hati - 2hatj - 2hatk`
    D
    `vecP = hati -3hatj + 2hatk, vecQ = 2hati - 2hatj + hatk`

  • Resultant of two vector of equal magnitude A is

    A
    `sqrt(3)Aat 60^(@)`
    B
    `sqrt(2)Aat 90^(@)`
    C
    `2Aat 120^(@)`
    D
    `Aat 180^(@)`

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