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Find direction consines of the line joinong $(2 , -3 , 1 )$and $(3 , 1 , -2 ).$

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  • The d.c.s of a vector with d.r.s $(a,b,c)$ are $\large\frac{a}{\sqrt{a^2+b^2+c^2}}, \large\frac{b}{\sqrt{a^2+b^2+c^2}}, \large\frac{c}{\sqrt{a^2+b^2+c^2}}$
Let $ A(2, -3, 1), \: B ( 3, 1, -2)$
Then $ \overrightarrow {AB} = \overrightarrow {OB} -\overrightarrow {OA} =(3-2)\overrightarrow i+(1+3)\overrightarrow j+(-2-1)\overrightarrow k$
$ = \overrightarrow i+4\overrightarrow j-3\overrightarrow k$
The d.r.s of $ \overrightarrow {AB} $ are $ (1,4,-3) $ and of $ \overrightarrow {BA} (-1, -4, 3)$
The d.c.s are $ \pm \bigg( \large\frac{1}{\sqrt{1+16+9}}, \large\frac{4}{\sqrt{1+16+9}},\large\frac{-3}{\sqrt{1+16+9}} \bigg)$
$= \pm \bigg( \large\frac{1}{\sqrt{26}}, \large\frac{4}{\sqrt{26}}, \large\frac{-3}{\sqrt{26}} \bigg)$
answered Jun 11, 2013 by thanvigandhi_1
 

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