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The unit vector in the direction of bar(...

The unit vector in the direction of `bar(x)=(-2,1,-2)` is …………..

A

`((2)/(3),-(1)/(3),(2)/(3))`

B

`(-(2)/(3),(1)/(3),-(2)/(3))`

C

`(-(2)/(9),(1)/(9),-(2)/(9))`

D

`((2)/(9),-(1)/(9),(2)/(9))`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • The unit vector in the opposite direction of bar(x)+bar(y)-2bar(z) is ………… where bar(x)=(1,1,0),bar(y)=(0,1,1) and bar(z)=(1,0,1) .

    A
    `((1)/(sqrt(6)),(-2)/(sqrt(6)),(1)/(sqrt(6)))`
    B
    `((1)/(6),(-2)/(6),(1)/(6))`
    C
    `((-1)/(sqrt(6)),(2)/(sqrt(6)),(-1)/(sqrt(6)))`
    D
    `((-1)/(6),(2)/(6),(-1)/(6))`

  • The unit vector in the direction 6hati-2hatj+3hatk is ………….

    A
    `(6)/(7)hati+(2)/(7)hatj+(3)/(7)hatk`
    B
    `(6)/(7)hati-(2)/(7)hatj+(3)/(7)hatk`
    C
    `(-6)/(7)hati+(2)/(7)hatj+(3)/(7)hatk`
    D
    `(6)/(7)hati+(2)/(7)hatj-(3)/(7)hatk`

  • If bar(a)=(1,1,1),bar(b)=(4,-2,3) and bar( c )=(1,-2,1) then the vector of magnitude 6 in the direction of 2bar(a)-bar(b)+3bar( c ) is ……………..

    A
    `((1)/(3),(-2)/(3),(2)/(3))`
    B
    (2, -4, 4)
    C
    `(-2, 4, -4)`
    D
    `((-1)/(3),(2)/(3),(-2)/(3))`

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    The vector with magnitude 17sqrt(2) and in the opposite direction of (0,1,-1) is …………..

    The direction cosines of bar( r )=(6,-2,3) are …………

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