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The Cartesian Equations of Line Are 3x+1=6y-2=1-z Find Its Equation in Vector Form. - Mathematics and Statistics

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The Cartesian equations of line are 3x+1=6y-2=1-z find its equation in vector form.

 

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Solution

Equation of given line is  3x+1=6y-2=1-z

Dividing throughout by 6, we get

`(3(x+1/3))/6=(6(y-1/3))/6=-(z-1)/(6)`

`(x+1/3)/2=(y-1/3)/1=-(z-1)/6`

direction ratios of the line are 2, 1, -6. Its vector equation is

`bar r=(hati+hatj+hatk)+lambda(2hati+hatj-6hatk)`

Concept: Equation of a Line in Space
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