Question

1. a) Write the vector and parametric equations of the line through the points A(6, -1, 5) and B(-2, -3, 6).

b) Find another point on the line in (a).

-----

This is what I got for a)

r = 6i-j+5k + t(-8i-2j+k)

x = 6-8t
y = -1-2t
z = 5+t

I need help with b)

Answer 1

a point on the line? Let t be any value, perhaps equal to say 1/2
then
x=6-4=2
y=-1-1=-2
z=5.5

Answer 2

Hi bobpursley,

I got 2 answers for a) but I'm not sure which one is correct, could you please help me determine which is correct?

the first answer I got is posted in this question, the second answer I got is this one for part a) could you please help me

for a) I got this instead:

vector equation:
[x, y, z] = [6, -1, 5] + t[-8, -2, 1]

parametric equation:
x=6+t(-2)
x=6-2t

y=-1+t(-3)
y=-1-3t

z=5+6t

and because I got this for part a), it also means my part b) changes too.. so i got this:

b) [x,y,z] = [6,-1,5] + t[-8,-2,1]
= [6,-1,5] + 1[-8,-2,1]
= [6,-1,5] + [-8,-2,1]
= 6-8, -1-2, 5+1
= (-2,-3,6)

please let me know which one is correct.. thank you!