alleryIf $(2,-3,6)$ are direction ratios of a line, then a set of direction cosines is
A$\left(\dfrac{2}{7},-\dfrac{3}{7},\dfrac{6}{7}\right)$
B$\left(\dfrac{2}{\sqrt{49}},-\dfrac{3}{\sqrt{49}},\dfrac{6}{\sqrt{49}}\right)$
C$\left(\dfrac{2}{\sqrt{13}},-\dfrac{3}{\sqrt{13}},\dfrac{6}{\sqrt{13}}\right)$
D$\left(\dfrac{2}{\sqrt{14}},-\dfrac{3}{\sqrt{14}},\dfrac{6}{\sqrt{14}}\right)$
Answer & Solution
Correct answer: A. $\left(\dfrac{2}{7},-\dfrac{3}{7},\dfrac{6}{7}\right)$
Direction cosines are obtained by dividing the direction ratios by their magnitude.
For $(2,-3,6)$, the magnitude is $\sqrt{2^2+(-3)^2+6^2}=\sqrt{49}=7$.
Hence the direction cosines are $\left(\dfrac{2}{7},-\dfrac{3}{7},\dfrac{6}{7}\right)$.
Option A and B are numerically the same, but A is the simplified standard form
since exactly one option must be correct, A is the intended answer.
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