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).
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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)
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
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!
To find another point on the line formed by the points A(6, -1, 5) and B(-2, -3, 6), you can choose any value for the parameter t and substitute it into the parametric equations you found in part a) to obtain the corresponding values of x, y, and z.
Let's choose t = 1 for simplicity. Substituting t = 1 into the parametric equations:
x = 6 - 8(1) = -2
y = -1 - 2(1) = -3
z = 5 + 1 = 6
Therefore, when t = 1, the corresponding coordinates are (-2, -3, 6), which gives us another point on the line formed by points A and B.