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Say there are two vectors $A$ and $B$ in $3D$.

to get the angle between the cross product of those two vectors, you use

$$||A\times B|| = ||A||\;||B||\sin(\theta). $$

right?

Is this equation equivalent to $||A\times B|| = AB$(dot product of $AB$) * sin(theta)?

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    $\begingroup$ no it's not ! $A\cdot B\neq \|A\|\|B\|$ in general. $\endgroup$
    – Surb
    Apr 23, 2016 at 14:07

1 Answer 1

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No to both questions.

  1. It's usually easier to use the dot product $A\cdot B = |A|\,|B|\,\cos\theta$.
  2. It is only equivalent if either $\sin\theta=0$ or $A\cdot B=|A|\,|B|$ which happens when $\cos\theta=1$.
    (So, almost never..)
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  • $\begingroup$ so you are saying ||AxB|| = ||A||*||B||*sin(theta). is wrong? Isn't this a proven formula? $\endgroup$
    – Hello
    Apr 23, 2016 at 14:09
  • $\begingroup$ No, this one I didn't say:) The formula is good, and you can actually use it to get $\theta$. But it is usually easier to use the dot product. $\endgroup$
    – Berci
    Apr 23, 2016 at 14:10
  • $\begingroup$ Ohhhh. Ok. Misunderstood you there. Thx for the answer! $\endgroup$
    – Hello
    Apr 23, 2016 at 14:11
  • $\begingroup$ No, they are saying that the formula $\|A\times B\|=\left|\,A\cdot B\,\right|\sin(\theta)$ is false, in general. $\endgroup$
    – robjohn
    Apr 23, 2016 at 14:11
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    $\begingroup$ No, "in general" as in "for most values of $\theta$". $\endgroup$
    – robjohn
    Apr 23, 2016 at 14:13

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