Question
Show that the vectors $\mathbf{a}=\mathbf{i}-\mathbf{j}, \mathbf{b}=\mathbf{i}+\mathbf{j}, \quad$ and$\mathbf{c}=2 \mathbf{k}$ are mutually orthogonal, that is, each pair of vectors is orthogonal.
Step 1
The dot product of two vectors is given by the sum of the products of their corresponding components. So, we have: \[\mathbf{a} \cdot \mathbf{b} =\langle 1,-1,0\rangle \cdot\langle 1,1,0\rangle =1(1)+(-1)(1)+0(0) =0\] Show more…
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