If the direction ratios of a line are 1, -3, | vedclass

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Question

(A) Given direction ratios are $a = 1, b = -3, c = 2$. The formula for direction cosines $(l, m, n)$ is given by: $l = \frac{a}{\sqrt{a^2 + b^2 + c^2}

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$\frac{1}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{2}{\sqrt{14}}$

Vedclass · Answer

(A) Given direction ratios are $a = 1, b = -3, c = 2$. The formula for direction cosines $(l, m, n)$ is given by: $l = \frac{a}{\sqrt{a^2 + b^2 + c^2}}, m = \frac{b}{\sqrt{a^2 + b^2 + c^2}}, n = \frac{c}{\sqrt{a^2 + b^2 + c^2}}$. First,calculate the magnitude: $\sqrt{a^2 + b^2 + c^2} = \sqrt{1^2 + (-3)^2 + 2^2} = \sqrt{1 + 9 + 4} = \sqrt{14}$. Now,calculate the direction cosines: $l = \frac{1}{\sqrt{14}}$,$m = \frac{-3}{\sqrt{14}}$,$n = \frac{2}{\sqrt{14}}$. Thus,the direction cosines are $\frac{1}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{2}{\sqrt{14}}$.

If the direction ratios of a line are $1, -3, 2$,find the direction cosines of the line.

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