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A vector vec( r ) has length 21 and dire...

A vector `vec( r )` has length 21 and directi9on ratio `2,-3,6`. Find the direction cosines and components of `vec( r )` given that `vec( r )` makes an acute angle with X- axis.

Text Solution

Verified by Experts

The correct Answer is:
Direction cosine:`2/7,-3/7,6/7`
Componants : `6hati-9hatj+18hatk`
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Knowledge Check

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

    A
    6, -2, 3
    B
    `(6)/(sqrt(7)),(-2)/(sqrt(7)),(3)/(sqrt(7))`
    C
    `(-6)/(7),(2)/(7),(-3)/(7)`
    D
    `(6)/(7),(-2)/(7),(3)/(7)`

  • For the vectors A(-1,-2,3) and B(1,2,-1) the direction cosines of vec(AB) are ……………

    A
    `(1)/(3),(2)/(3),(-2)/(3)`
    B
    2, 4, -4
    C
    `(2)/(sqrt(6)),(4)/(sqrt(6)),(-4)/(sqrt(6))`
    D
    `(-1)/(3),(-2)/(3),(2)/(3)`

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