3. Vector \(\mathbf { v } = a \mathbf { i } + 0.6 \mathbf { j }\), where \(a\) is a constant.
- Given that the direction of \(\mathbf { v }\) is \(45 ^ { \circ }\), state the value of \(a\).
- Given instead that \(\mathbf { v }\) is parallel to \(8 \mathbf { i } + 3 \mathbf { j }\), find the value of \(a\).
- Given instead that \(\mathbf { v }\) is a unit vector, find the possible values of \(a\).
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