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# For what value of 'a' the vectors $2\hat i - 3\hat j + 4\hat k$ and $a\hat i + 6\hat j - 8\hat k$ are collinear?

Toolbox:
• Two or more vectors are said to be collinear if their magnitudes are equal or proportional.
Given vectors $2\hat i-3\hat j+4\hat k$ and $a\hat i+6\hat j-8\hat k$ are collinear
Equating the coefficients of $\hat i$ and $\hat j$ and $\hat k$ we get,
$\large\frac{2}{a}=\frac{-3}{6}=\frac{4}{-8}$
$\Rightarrow \large\frac{2}{a}=-\frac{1}{2}$
$\Rightarrow a=-4$