Given the two vectors \(\mathbf{a}\) and \(\mathbf{b}\) of the Question 8 express their sum, difference, scalar product and vector product in Cartesian coordinates. What is the angle \(\alpha\) between them?

Question 8

Find the vector \(\mathbf{c}\) which added to the vectors \(\mathbf{a}=(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})\) and \(\mathbf{b}=(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}})\) gives as a resultant \(\mathbf{r}=(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+1 \hat{\mathbf{k}})\)