# 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.

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.

### 5 Answers

- nbsaleLv 62 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

- VamanLv 72 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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- Jeffrey KLv 62 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