Find the direction cosines (d.cs) of directed line $O P$ if coordinates of $P$ is $(2, 3, 7)$ , $O$ being the origin.

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Solution

To find the direction cosines of the the line $O P$ where co-ordinates of $O$ and $P$ are $(0, 0, 0)$ and $(2, 3, 7)$ respectively.
Now the direction co-sine of the line $O P$ is
$(\frac{2 - 0}{\sqrt{2^{2} + 3^{2} + 7^{2}}}, \frac{3 - 0}{\sqrt{2^{2} + 3^{2} + 7^{2}}}, \frac{7 - 0}{\sqrt{2^{2} + 3^{2} + 7^{2}}}) = (\frac{2}{\sqrt{62}}, \frac{3}{\sqrt{62}}, \frac{7}{\sqrt{62}})$ .

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Find the direction cosines (d.cs) of directed line OP if coordinates of P is (2,3,7), O being the origin.

To find the direction cosines of the the line OP where co-ordinates of O and P are (0,0,0) and (2,3,7) respectively.Now the direction co-sine of the line OP is (2−0√22+32+72,3−0√22+32+72,7−0√22+32+72)=(2√62,3√62,7√62).

Find the direction cosines (d.cs) of directed line $O P$ if coordinates of $P$ is $(2, 3, 7)$ , $O$ being the origin.