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