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Question 3

If a line has the direction ratios −18, 12, −4, then what are its direction cosines?

Answer

If a line has direction ratios of −18, 12, and −4, then its direction cosines are

\begin{align} \frac{-18}{\sqrt {(-18)^2 + (12)^2 + (-4)^2}},\frac{12}{\sqrt {(-18)^2 + (12)^2 + (-4)^2}},\frac{-4}{\sqrt {(-18)^2 + (12)^2 + (-4)^2}}\end{align}

\begin{align} i.e., \frac{-18}{22},\frac{12}{22},\frac{-4}{22}\end{align}

\begin{align}  \frac{-9}{11},\frac{6}{11},\frac{-2}{11}\end{align}

Thus, the direction cosines are 

\begin{align} \frac{-9}{11},\frac{6}{11} and \frac{-2}{11}\end{align}

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