Find the shortest distance between the given lines. Find the shortest distance and the vector equation of the line of shortest distance between the lines given by: r → = ( 8 + 3 λ ) i ^ - ( 9 + 16 λ ) j ^ + ( 10 + 7 λ ) k ^ a n d r → = 15 i ^ + 29 j ^ + 5 k ^ + μ ( 3 i ^ + 8 j ^ - 5 k ^ ) Share with your friends Share 1 Shruti Tyagi answered this Dear student, We know that,Shortest distance between the line is d=a2→-a1→.b1→×b2→b1→×b2→Step 1:-The given lines areL1: r→=8+3λi^-9+16λj^+10+7λk^L2: r→=15i^+29j^+5k^+μ3i^+8j^-5k^Let L1 can be written asr→=8i^-9j^+10k^+λ3i^-16j^+7k^The shortest distance between the line isd=a2→-a1→.b1→×b2→b1→×b2→Here, a1=8i^-9j^+10k^a2=15i^+29j^+5k^b1=3i^-16j^+7k^b2=3i^+8j^-5k^Let us obtain a2→-a1→a2→-a1→=15i^+29j^+5k^-8i^-9j^+10k^=15i^+29j^+5k^-8i^+9j^-10k^=7i^+38j^-5k^Step 2:Next let us obtain b1→×b2→b1→×b2→=i^j^k^3-16738-5=i^80-56-j^-15-21+k^24+48=24i^+36j^+72k^=122i^+3j^+6k^b1→×b2→=22+32+62=4+9+36=7Step 3:Now substituting the respective values we get,d=7i^+38j^-5k^.24i^+36j^+72k^84=168+1368-36084=117684=14Hence the shortest distance between the line is 14 Regards 0 View Full Answer