Question

PLEASE HELP WITH THIS VECTORS PROBLEM!



a) Write a vector equation and parametric equations of the line through
P(3 , 5) and Q(-4 , 7).

b) Write the scalar equation of the line with parametric equations:
x=6-7t , y=-2+3t

Please show all work, Thanks (:

Answer 1

First work out the vector through those two points P and Q

Q(-4, 7) - P(3, 5)

vector QP = (3 - (-4) , 5 - 7) = (7, -2)

Now that we have a vector we simply write the vector equation

the general form of the vector equation is

(x,y) = Xo + t(v)

(x,y) = (-4,7) + t(7, -2) **** This is the vector equation

To obtain parametric equation, you simply break down the above equation for x and y

x = -4 + 7t
y = 7 -2t

Answer 2

When does part a) end?

Answer 3

that is part A, Im not sure about part B

Answer 4

Oh, so the answer is x = -4 + 7t
y = 7 -2t?

Answer 5

@javawarrior ?

Answer 6

yes those are the parametric equations

Answer 7

Thanks :)
How do we do part b)?

Answer 8

From my part of the world, the scalar equation is referred to as the general equation.

simply take these equations:

x=6-7t
y=-2+3t

and try to eliminate t

The general form the equation should be Ax + By = D

Answer 9

How do we eliminate t?

Answer 10

just take a multiple of one equation and minus the other to get rid of t

Answer 11

Can you take me through it?

Answer 12

@javawarrior ?

Answer 13

@lgbasallote can you solve those 2 equations to eliminate T ?