# Why are the vectors canceled out in this scenario for angular momentum of a particle?

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,

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!

• Note that $\hat j \times \hat i\ne \hat k$ rather $\hat j \times \hat i = - \hat k$ – Farcher May 21 at 6:42

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.