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Find the unit vector in the direction of...

Find the unit vector in the direction of the vector `veca=hati+hatj+2hatk`.

Text Solution

Verified by Experts

The unit vector `veca` in the direction of vector
`veca=hati+hatj+2hatk` is given by `hata=(veca)/(|a|)`.
`" "|veca|=sqrt(1^(2)+1^(2)+2^(2))=sqrt(1+1+4) =sqrt(6)`
`therefore" "hata=(veca)/(|veca|)=(hati+hatj+2hatk)/(sqrt(6)) = (1)/(sqrt6) hati+(1)/(sqrt6) hatj+(2)/(sqrt6) hatk`
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Find the unit vector in the direction of the sum of vectors , veca=2hati+2hatj-5hatkandvecb=2hati+hatj+3hatk .

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Knowledge Check

  • The unit vector in the direction of vecA=hati+hatj+hatk is

    A
    `hati+hatj+hatk`
    B
    `(hati+hatj+hatk)/(sqrt2)`
    C
    `(hati+hatj+hatk)/(sqrt3)`
    D
    `(hati+hatj+hatk)/(sqrt6)`
  • The unit vector in the direction of vecA=hati+hatj+hatk is

    A
    `hati+hatj+hatk`
    B
    `(hati+hatj+hatk)/(sqrt(2))`
    C
    `(hati+hatj+hatk)/(sqrt(3))`
    D
    `(hati+hatj+hatk)/(sqrt(6))`
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