If the Cartesian equations of a line are ` (3-x)/5=(y+4)/7=(2z-6)/4` , write the vector equation for the line.

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#### Solution

The equation can be rewritten as :

`(3-x)/5=(y+4)/7=(z-3)/2`

Hence the vector equation of the line is

`vecr=3hati-4hatj+3hatk+lamda(-5hati+7hatj+2hatk)`

Concept: Equation of a Line in Space

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