Math repost (please check)
posted by Mary .
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((P2P1) 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`= P2P1
P`= (3,2,3)
L2
P`= P4P3
P`= (3.5,2,6.5)
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