What does it mean when A(dot)(B x C) = -A(dot)(B x C)?

I met with a tutor today and she said that since LHS = -(LHS) then these vector expressions must both be equal to zero.

Did some googling but can't find why this is so. Thanks in advance.

Update:

This was a problem on my exam which stated that we were to assume that LHS was indeed equal to the RHS, that is LHS = -(LHS). So it was incorrect to simply say that "LHS is not equal to the RHS" which is why I got the problem wrong.

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  • alex
    Lv 7
    2 years ago
    Best Answer

    LHS = -(LHS)

    --->

    LHS + (LHS) = 0

    2(LHS) = 0

    or

    LHS = 0

  • nbsale
    Lv 6
    2 years ago

    Why google it? Just work it out, since it's very straightforward.

    Let A = <a_i> and BXC = <d_i>

    Then the dot products give you

    sum (a_i times d_i) = k

    sum (-a_i time d_i) = -k but that = k also.

    k = -k

    Add k to both sides:

    2k = 0

    divide by 2

    k = 0

  • Como
    Lv 7
    2 years ago

    A • ( B x C ) + A • ( B x C ) = 0

    A • ( B x C ) = 0

  • Vaman
    Lv 7
    2 years ago

    Since sum is 0 we can stay that A is perpendicular to BxC. Here A, B C should be vectors.

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  • 2 years ago

    If vectors A, B, C are in the same plane, then this expression is zero. B x C yields a vector perpendicular to the plane that B and C lie in. The dot product of perpendicular vectors is zero.

    So A . B x C = 0

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