[All Steps] (a) Determine all values α ∈ R 0 such that the vectors <1/3, (alpha)/(3), 2>,< 17 • α-17,17 • α^2,-17 •
Question: (a) Determine all values \(\alpha \in \mathbb{R} \backslash\{0\}\) such that the vectors
\[\left\langle\frac{1}{3}, \frac{\alpha}{3}, 2\right\rangle,\left\langle 17 \cdot \alpha-17,17 \cdot \alpha^{2},-17 \cdot \alpha+\frac{17}{6}\right\rangle \in \mathbb{R}^{3}\]are orthogonal.
(b) Determine a unit vector \(\mathbf{v} \in \mathbb{R}^{3}\), i.e., a vector of length one, that is orthogonal to both \(\langle 0,42,42\rangle\) and \(\pi \cdot \mathbf{i}-\pi \cdot \mathbf{k}\).
(c) Let \(\mathbf{v} \in \mathbb{R}^{3} \backslash\{0\}\), and let \(\mathbf{x}, \mathbf{y} \in \mathbb{R}^{3}\) such that
\[\mathrm{x} \times \mathbf{v}=\mathbf{y} \times \mathbf{v}\]Does this imply \(\mathrm{x}=\mathrm{y}\) ? Justify your answer.
Deliverable: Word Document 
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[See] (a) Determine a vector equation r(t)=\mathrmr_0+t •
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