Question

L1=P1(1,3,5) and P2(4,5,2)

L2=P4(-1,6,-3) and P3(points not given)


a. Find the equations of lines L1 and L2. P3 is the midpoint of L1, that is, u=0.5 at P3.

P(u)=P1 + u((P2-P1) 0 which is less than or equal to (u)which is less than or equal to 1.

L1= P(u)= (1,3,5) + u(3,2,-3)

L2= P(u)= (2.5,4,3.5)+ v(-3.5,2,-6.5)

b. Find a point on each vector for each line where u=0.25.

L1
2.5 +1= (3.2/2)=1.75
4 + 3 = (7/2)= 3.5
3.5 + 5= (8.5/2)=4.25

L2
0.75+(-1)= (-0.25/2)= -0.125
5+ 6= (11/2)= 5.5
0.25 + (-3)= (-2.75/2) = -1.375

ans= when u =0.25 on L1 the points are (1.75,3.5,4.25). When u=0.25 on L2 the points are (-0.125,5.5,-1.375).

c. Find the tangent vector for each line. Are they constant? What is your conclusion.

L1
P`= P2-P1
P`= (3,2,-3)

L2
P`= P4-P3
P`= (-3.5,2,-6.5)