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Write the direction - cosines of the line joining the points (1,0,0) and (0,1,1).

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  • The cosines of the angle made by the vector with the coordinate axes is called direction cosines.
  • D.C of vector, $x\hat i+y\hat j+z\hat k\:is\:(\large\frac{x}{\sqrt{x^2+y^2+z^2}},\frac{y}{\sqrt{x^2+y^2+z^2}},\frac{z}{\sqrt{x^2+y^2+z^2}})$
Step 1:
The direction ratios of the line joining these points are $(x_2-x_1),(y_2-y_1),(z_2-z_1)$
(i.e) $(0-1),(1-0),(1-0)$
$\Rightarrow (-1,1,1)$
Step 2:
Its direction cosines are $-\large\frac{1}{\sqrt{1^2+1^2+1^2}},\frac{1}{\sqrt{1^2+1^2+1^2}},\frac{1}{\sqrt{1^2+1^2+1^2}}$
$\Rightarrow \large\frac{-1}{\sqrt 3},\frac{1}{\sqrt 3},\frac{1}{\sqrt 3}$
answered Nov 12, 2013 by sreemathi.v

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