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If vec(a)+vec(b)+vec(c )=0 " and" |vec(a...

If `vec(a)+vec(b)+vec(c )=0 " and" |vec(a)|=3,|vec(b)|=5, |vec(c )|=7`, then find the value of `vec(a)*vec(b)+vec(b)*vec(c )+vec(c )*vec(a)`.

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To solve the problem step by step, we start with the given information: 1. **Given**: \[ \vec{a} + \vec{b} + \vec{c} = 0 \] and the magnitudes: \[ ...
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Knowledge Check

  • If vec(a), vec(b), vec(c ) are three vectors such that vec(a) + vec(b) + vec(c ) = 0 and | vec(a) | =2, |vec(b) | =3, | vec(c ) = 5 , then the value of vec(a). vec(b) + vec(b) . vec( c ) + vec(c ).vec(a) is

    A
    0
    B
    1
    C
    38
    D
    `-19`

  • If vec(a) , vec( b) and vec( c ) are unit vectors such that vec(a) + vec(b) + vec( c) = 0 , then the values of vec(a). vec(b)+ vec(b) . vec( c )+ vec( c) .vec(a) is

    A
    1
    B
    `(3)/(2)`
    C
    `- (3)/(2)`
    D
    none of these

  • If vec(a) + vec(b) + vec( c ) = vec(0), |vec(a) | = sqrt( 37), | vec(b)| =3 and | vec( c)| =4 , then the angle between vec(b) and vec(c ) is

    A
    `90^(@)`
    B
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    C
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