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Section 5-3 : Dot Product

8. Determine if \(\vec w = \vec i + 4\vec j - 2\vec k\) and \(\vec v = - 3\vec i - 12\vec j + 6\vec k\) are parallel, orthogonal or neither.

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Based on a quick inspection is seems (hopefully) fairly clear that we have,

\[\vec v = - 3\vec w\]

Therefore, the two vectors are parallel.

On a side note an alternate method for working this problem is to find the angle between the two vectors and using that to determine the answer.

Depending on which method you find easiest either will get you the correct answer.