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Find the equations of the line passing through the point (1,-2,3) and parallel to the line `(x-6)/(3) =(y-2)/(-4) =(z+7)/(5)` Also find the vector for

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Find the equations of the line passing through the point (1,-2,3) and parallel to the line `(x-6)/(3) =(y-2)/(-4) =(z+7)/(5)`
Also find the vector form of this equations so obtained .
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Correct Answer - `(x-1)/(3)=(y+2)/(-4) =(z-3)/(5) , vec( r) =(hat(i) -2hat(j) +3hat(k)) +lambda (3hat(i) -4hat(j) +5hat(k))`
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