Solve the following problems a We have two lines here given

Solve the following problems: (a) We have two lines here, given by equation L1; {x = 1 + t y = -2 + 3t z = 4 - t L2: {x = 2s y = 3 + s z = -3 + 4s Please show upsilon_1 and upsilon_2 (upsilon_1 is the direction vector for L_1 and upsilon_2 for L_2). Based oil the information of upsilon_1 and upsilon_2, are L_1 and L_2 parallel to each other? Continue from (a), do L_1 and L_2 intersect? You need to show all relevant work. If your answer is yes, what is the point of intersection? Plug this point back into both equation L_1 and L_2 see if it makes any sense. Do you still believe they intersect? If your answer is no, show proper work to justify your answer. Continue from (b), if you still insist L_1 and L_2 intersect, then their distance is 0. Would you like to claim so? If you think they do not intersect, then depending on your answer from part (a) and part (b), they are either parallel or skewed. In either case, find the distance between L_1 and L_2.

Solution

V1=(1,3,-1)

V2 =(2,1,4)