Length of projection-confused with whether to use cross or dot product

Hi Mr Koh it's XXX. I have a question for you:  Why did the teacher use cross product instead of dot product? Thank you.

Hi,

The way the respective dot and cross product results arise are attributed to the orientation of the known direction vector. In the context you cited, the known direction vector, ie the normal to the plane is vertically placed, hence things are phrased as such.  On the other hand, if you consider the typical projection of a given vector onto a line, the known direction vector d is seen running horizontally instead of vertically. Therefore, the dot and cross product results are switched. I have crafted two separate diagrams (attached below) for your reference, hopefully that will clarify matters.

Best Regards,

Mr Koh