Question

what is the angle beteen unit vector i+j and i-j?

Answer 1

Dear Student,

Assume that
$$\begin{gathered} \overrightarrow{A}=i+j,\overrightarrow{B}=i-j \\ \overrightarrow{A}.\overrightarrow{B}=AB\cos \theta \\ \Rightarrow \cos \theta =\frac{\overrightarrow{A}.\overrightarrow{B}}{AB}=\frac{i.i-i.j-j.j+j.i}{\sqrt{2}\sqrt{2}}=\frac{1-0-1+0}{2}=0 \\ \cos \theta =0=\cos 90 \\ \Rightarrow \theta ={90}^0 \end{gathered}$$