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### Section 11.2 : Vector Arithmetic

6. Determine if $$\vec v = 9\vec i - 6\vec j - 24\vec k$$ and $$\vec w = \left\langle { - 15,10,40} \right\rangle$$ are parallel vectors.

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Recall that two vectors are parallel if they are scalar multiples of each other. In other words, these two vectors will be scalar multiples if we can find a number $$k$$ such that,

$\vec v = k\,\vec w$ Show Step 2

Let’s just take a look at the first component from each vector. It is should be clear that $$- 15 = \left( { - \frac{5}{3}} \right)\left( 9 \right)$$. So, to convert the first components we’d need to multiply $$\vec v$$ by $$- \frac{5}{3}$$ .

if we did that we’d get,

$- \frac{5}{3}\vec v = \left\langle { - 15,10,40} \right\rangle = \vec w$

So, we were able to find a number $$k$$ that we could use to convert $$\vec v$$ into $$\vec w$$ through scalar multiplication and so the two vectors are parallel.