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I have a study guide for our next test, and I'm trying to understand the professors answer but I don't understand why i^ * i^ = 0?

Here is his work, enter image description here

Why do we know that the P Vector is on direction i^? Why does it cancel out the other i^ direction once multiplied? I appreciate any and all help in understanding this, thank you!

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  • $\begingroup$ Note that $\hat j \times \hat i\ne \hat k$ rather $\hat j \times \hat i = - \hat k$ $\endgroup$ – Farcher May 21 at 6:42
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The vectors cancel because your professor is taking the cross product between them, $\hat{\bf i}\times\hat{\bf i}$, rather than the scalar product, $\hat{\bf i}\cdot\hat{\bf i}$. The cross product between two parallel vectors, (or two of the same vectors) is always zero.

With regard to your second question, the momentum vector $\bf P$ is in the $\hat{\bf i}$ direction because the velocity vector $\bf v$ is in this direction, and ${\bf P}=m{\bf v}$, where $m$ is the mass of the object.

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