Question

find a vector equation and parametric equations for the line through point (0,14,-10) and parallel to the line x=-1+2T, y=6-3T, Z=3+9T

Answer 1

parallel have same vector parts; just different point parts

Answer 2

x = -1+2t
y = 6-3t
z = 3+9t

strip off the old point (-1,6,3)

x = Px+2t
y = Py-3t
z = Pz+9t

and add in the new point (0,14,-10)

x = 0+2t
y = 14-3t
z = -10+9t

and we get the parametric

Answer 3

what a vector equation look like? is the that v = i+j+k stuff?

Answer 4

what does the 2T, -3T and 9T represent?

Answer 5

yes it is

Answer 6

the vector <2,-3,9> strecthed to any scalar "t"

Answer 7

to form a line; its just a vector attached to a pointand strecthched to hit all point on the line

Answer 8

v = t(2i -3j +9) maybe?

Answer 9

i got no idea how your text formats a vector equation, but its pretty basic from that i believe

Answer 10

okay how would i do it if it was perpendicular instead of parallel?

Answer 11

the perp vector has to dot with the original vector and get 0

Answer 12

2,-3,9
a, b, c
-------
2a-3b+9c = 0

Answer 13

okay still kinda confused, i'll ask another question on it hang on

Answer 14

there are infinelty many perp vector to a line; they form a plane all around it