A calculus problem by Mohsin Khan

Calculus Level 2

In $\mathbb{R}^3$ , $\widehat{i} \cdot \widehat{i}$ is equal to

1 0 -2 -1

1 solution

Micah Wood
Nov 18, 2014

Let unit vector $\mathbf{u}=\mathbf{\hat i} = \langle \mathbf{u}_1, \mathbf{u}_2, \mathbf{u}_3 \rangle$

We know that $||\mathbf{u}|| = \sqrt{\mathbf{u}_1^2+\mathbf{u}_2^2+\mathbf{u}_3^2}=1$

So we have $\mathbf{u}\cdot\mathbf{u} = \mathbf{u}_1^2+\mathbf{u}_2^2+\mathbf{u}_3^2 = ||\mathbf{u}||^2= \boxed{1}$