Vectors

Problem

The Problem

Let $ec{u} = (1, 2, 3)$ and $ec{v} = (4, -1, 0)$ .

Compute the dot product $ec{u} cdot ec{v}$ .
Compute the cross product $ec{u} imes ec{v}$ .
Find the angle $h e t a$ between $ec{u}$ and $ec{v}$ (you may leave it as $co s^{- 1} (c d o t)$ ).
Find the projection of $ec{u}$ onto $ec{v}$ .

These are the bread and butter of any quant interview warm-up. If you fumble the cross product, you'll fumble the rest of the day.