The shortest distance between the lines: x-1/alpha= y+1/-1 =​​z/1,(alpha not equal to -1) x+y+z+1=0= 2x-y+z+3 is 1/rt3, then alpha=? [32/19]

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Please find below the solution to the asked query:

We havex-1α=y+1-1=z1So we havex1,y1,z1=1,-1,0Point through which line passesDirection ratios area1,b1,c1=α,-1,1andx+y+z+1=0=2x-y+z+3i.e.x+y=-z-1...i2x-y+z+3=02x-y=-z-3...iii+iix+y+2x-y=-z-1-z-33x=-2z-4 x=-2z-433x+4-2=z-2z-43+y=-z-1y=2z+43-z-1y=2z+4-3z-333y=-z+13y-1=-zz=3y-1-1Hence we have3x+4-2=3y-1-1=z1i.e.x+43-23=y-13-13=z1So x2,y2,z2=-43,13,0Direction ratios is given bya2,b2,c2=-23,-13,1Shortest distance is given by

Shortest distance=13-43-113+10α-11-23-131-1+132+-23-α2+-α3-232=13-73430α-11-23-131=13-232+-23-α2+-α3-232-73-1+13-43α+23=13-232+23+α2+α3+232-7323-433α+23=13-232+23+α2+α3+232-159-12α9-89=13-232+23+α2+α3+232-23-12α9=13-232+2+3α32+α+232Square both sides and solve for α to get your answer

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