Question

Please help teach me to solve this question on parallel vectors (Thankyou in advance):
Consider the points P(-3,1,0,5), Q(0,2,1,-3), and R(-2,1,4,0). Find the point S in R4 whose third component is 8 and such that PQ is parallel to RS. S = ( ?, ?, 8, ?)

Answer 1

this should help you solve your problem: http://mathworld.wolfram.com/ParallelVectors.html

Answer 2

a vector can be thought of as a line in space.

lines that are parallel have the same slope.

P-Q = vector vector, or slope, from P to Q

P(-3,1, 0,5)
-Q( 0, 2,1,-3)
------------
V(-3,-1,-1,8)

any scaled value of this vector, when attached to any point, will give you a parallel "line".

The point given is R:

R(-2,1,4,0) + V(-3,-1,-1,8)

x=-2-3t
y= 1-1t
z= 4-1t
m= 0+8t

Now, we can find any point we want to on this line

Answer 3

since they want Z to be 8:

z= 4-1t = 8
-t = 4

t = -4 will gives us the rest of them