Question

determine whether u and v are orthogonal, parallel, or neither.
u = \langle - 2,6 \
angle, v = \langle - 1,3 \
angle

Explanation:

Step1: Check for parallel

Check if \(\mathbf{u} = k\mathbf{v}\) for some scalar \(k\).
For \(\mathbf{u}=\langle - 2,6
angle\) and \(\mathbf{v}=\langle - 1,3
angle\), if \(-2=k\times(-1)\) and \(6 = k\times3\).
From \(-2=-k\), we get \(k = 2\). From \(6 = 3k\), we get \(k=2\).

Step2: Check for orthogonal

Check the dot - product \(\mathbf{u}\cdot\mathbf{v}=(-2)\times(-1)+6\times3\).

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Answer:

Since \(\mathbf{u} = 2\mathbf{v}\), \(\mathbf{u}\) and \(\mathbf{v}\) are parallel.