# Cross product angle formula

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)?

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

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..)
• so you are saying ||AxB|| = ||A||*||B||*sin(theta). is wrong? Isn't this a proven formula? Apr 23, 2016 at 14:09
• 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. Apr 23, 2016 at 14:10
• Ohhhh. Ok. Misunderstood you there. Thx for the answer! Apr 23, 2016 at 14:11
• No, they are saying that the formula $\|A\times B\|=\left|\,A\cdot B\,\right|\sin(\theta)$ is false, in general.
– robjohn
Apr 23, 2016 at 14:11
• No, "in general" as in "for most values of $\theta$".
– robjohn
Apr 23, 2016 at 14:13