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If magnitude of sum of two unit vectors ...

If magnitude of sum of two unit vectors is `sqrt2` then find the magnitude of subtraction of these unit vectors.

Text Solution

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The correct Answer is:
`sqrt2`
`because |hat A + hatB|= sqrt2 rArr 2xx1 xx cos""(theta )/(2) = sqrt2`
`rArr cos ""(theta)/(2) = (1)/(sqrt2) rArr (theta )/( 2) = 45^(@) rArr theta = 90^(@)`
`" "|hatA- hatB|= 2xx1 xx sin""(theta)/(2) = 2 xx sin 45^(@) = sqrt2`
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