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Show that the vectors \(2\hat i − 3\hat j + 4\hat k\) and \(− 4\hat i + 6\hat j − 8\hat k\) are collinear.

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  • Two vectors are said to be collinear if they are parallel or have same direction.
Step 1:
Let $\overrightarrow{a}=2\hat i-3\hat j+4\hat k$
$\;\;\;\overrightarrow b=-4\hat i+6\hat j-8\hat k$
If we take -2 as the common factor from $\overrightarrow b$ we get
$\overrightarrow b=-2(2\hat i-3\hat j+4\hat k)$
Step 2:
Now we can see that $\overrightarrow a$ and $\overrightarrow b$ have the same direction.
Hence they are collinear vectors.
answered May 17, 2013 by sreemathi.v

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