Answer to Question #135450 in Analytic Geometry for Gabsile

Question

Suppose u = (u1; u2; u3) :

Prove that

u x u = u²₁+ u²₂+ u²₃

Answer 1

Let $\vec{u} = u_1\hat{i} + u_2\hat{j}+u_3\hat{k}$

Then $u.u = (u_1\hat{i} + u_2\hat{j}+u_3\hat{k}).(u_1\hat{i} + u_2\hat{j}+u_3\hat{k}) = u_1^2 + u_2^2+u_3^2$