1.

Find the equation of the line passing through the points (1, 2, 3) and (-1, 0, 4).

Answer» Since line is passing through the points `A(1, 2, 3) and B(-1, 0, 4)`, it is along the vecor `vec(AB)= -2hati-2hatj+hatk`.
Hence, equation of line is
`" "vecr=hati+2hatj+3hatk+lamda(-2hati-2hatj+hatk)`
or `" "vecr=-hati+4hatk+lamda(-2hati-2hatj+hatk)`
`rArr" "(x-1)/(-2)=(y-2)/(-2)=(z-3)/(1)`
or `" "(x+1)/(-2)=(y-0)/(-2)=(z-4)/(1)`


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