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Test for Collinearity of Vectors

If the vector...

Question

If the vectors $2^i - q^j + 3^k$ and $4^i - 5^j + 6^k$ are collinear, then find the value of $q$ .

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Solution

Vectors are collinear, so
$\frac{2}{4} = \frac{- q}{- 5} = \frac{3}{6}$
So, $\frac{q}{5} = \frac{1}{2} q = \frac{5}{2} = 2.5$

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