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Are the lines frac[x][1]=frac[y][2]=frac...

Are the lines `frac[x][1]=frac[y][2]=frac[z][3]` and `frac[x-1][-2]=frac[y-2][-4]=frac[z-3][-6]` parallel?

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Find the shortest distance between the lines frac[x][2]=frac[y][-3]=frac[z][1] and frac[x-2][3]=frac[y-1][-5]=frac[z+2][2] .

Prove that the lines frac[x+3][2]=frac[y+5][3]=frac[z-7][-3] and frac[x+1][4]=frac[y+1][5]=frac[z+1][-1] are coplanar. Find the equation of plane containing them.

Solve frac[dx][dy]=frac[3x-7y+7][3y-7x-3]

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Find the equation of the plane passing through the line frac[x+1][-3]=frac[y-3][2]=frac[z+2][1] and the point (0,7,-7). Also show that the line x=frac[7-y][3]=frac[z+7][2] lies in this plane.

Integrate int(frac[x-1][2x+1])dx

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