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If hat a and hat b are unit vectors in...

If `hat a` and `hat b` are unit vectors inclined at an angle θ then prove that : `tan (θ/2) =|hat a + hat b|/ |hat a − hatb|`

Text Solution

Verified by Experts

The correct Answer is:
A
`(fogogof) (x)= sin^(2) (sin x^(2))`
`(gogof) (x) = sin (sin x^(2))`
`:. Sin^(2) (sin x^(2))= sin (sin x^(2))`
`rArr sin (sin x^(2)) [sin (sin x^(2))-1]=0`
`rArr sin (sin x^(2))=0` or `1`
`rArr sin x^(2) = npi` or `2 mpi+pi//2`, where `m, n in I`
`rArr sin x^(2)=0`
`rArr x^(2) =n pi rArr x= pm sqrt(npi), n in {0, 1, 2, ...}`.
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If hat a , hat b ,a n d hat c are unit vectors, then | hat a- hat b|^2+| hat b- hat c|^2+| hat c- hat a|^2 does not exceed

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Knowledge Check

  • The unit vector in the direction of the sum of vectors hat i + hat j + hat k and 2 hat i + 3 hat j + 4 hat k is

    A
    `(1)/(5sqrt2)(3 hat i + 4 hat j + 5 hat k)`
    B
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    C
    `(1)/(2 sqrt2)(4 hat i + 3 hat j + 5 hat k)`
    D
    `(1)/(3sqrt2(-3 hat k + 4 hat i + 5 hat j)`

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