Question

The direction of cosines of the line passing through the points (-2,4,-5),(1,2,3)​

Answer 1

Solution

$\sf we \: know \: the \: direction \: cosines \: of \: the \: line \: passing \: \\ \sf through \: two \: points \: p( x_{1} ,\: y_ 1 ,\: z_ 1) \: and q\: (x_ 2, \: y_ 2, \:z _ 2) are \: given \: by \\ \\ \bf \frac{x \:_ 2 - x_ 1}{pq}, \: \: \frac{y_ 2 - y_ 1}{pq} ,\: \: \frac{ \:z_ 2 - z_ 1}{pq}, \\ \\ \bf pq = \sqrt{(x_ 2 - x_ 1) + (y_ 2 - y_ 1) + (z_ 2 - z_ 1)} \\ \\ \\ \sf here \: \: p \: is \: ( - 2,4 ,- 5) \: and \: (1,2,3) \\ \\ \bf \: pq \: = \sqrt{ {( 1 - ( - 2)) }^{2} + {(2 - 4}^{2} ) + (3 - ( - 5))^{2}} = \sqrt{77} \\ \\ \sf \: thus \: the \: direction \: cosines \: of \: the \: line \: joining \: two \: points \: is \: \\ \frac{3}{ \sqrt{77} } , \: \frac{ - 2}{ \sqrt{77} } , \: \frac{8}{ \sqrt{77} }$

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Answer 2

The direction of cosines of the line passing through the points (-2,4,-5),(1,2,3)