Question

Determine a vector equation for each line:


a) Parallel to the x-axis and through P0(3 , -8)
b) Perpendicular to 4x-3y=17 and through P0(-2 , 4)
c) With the same x-intercept as [x , y , z] = [3 , 0 , 0] + t[4 , -4 , 1] and the same z-intercept as [x , y , z] = [6 , -2 , -3] + t[3, -1 , -2]

Please show all work! Thanks :)

Answer 1

a) <t+3,t-8>

Answer 2

How did you do that?

Answer 3

if you let t=0 the vector point2 at (3,-8)

Answer 4

points*

Answer 5

The answer for a) is [x,y] = [3, -8] + t[1,0]

Answer 6

Thats what the answer says, but how do you get that

Answer 7

Can you show your work?

Answer 8

Oh yes.. i forgot that is parallel to x-asix.
So, it is changing along x, no chnages along y.

Answer 9

How do we do it?

Answer 10

b)[-2,4,t]

Answer 11

HOW DO YOU SOLVE IT?

Answer 12

is this Linear Algerba? If so, this class is all about concept. Everything has to be done by thinking.

Answer 13

This is Grade 12 Calculus and vectors, chapter 8: Equations of Lines in Two-Space and Three-Space

Answer 14

For b, The plane equation is parallel to xy-plane, so, the vector that is othgonal to the plane is only along z-axis.
So, i let k be changing.

Answer 15

Is there any way to show your work for a)?

Answer 16

[t,0]+[3,-8] since x componet is the one only be changing.

Answer 17

+[3,-8] is because we have to let it touches the point.

Answer 18

So If I just wrote the answer as [x,y] = [3, -8] + t[1,0] without any other work shown, would I get full marks?

Answer 19

yes. because usually setting up equation has not much work to show.
Maybe you should have the answer [t+3,-8]

Answer 20

ok for part b) the answer is : [x,y] = [-2, 4] + t[-4,3]

Answer 21

Any work to show?

Answer 22

Hello?

Answer 23

for the given plane quation 4x-3y=17 has a normal vector [4,-3] by looking.
Then we use the normal vector form the othgonal equation by muliplying -1.
So, we get[-4,3] which is a vector that perpendicular to the given line.
You should have it write in [-4t-2,3t+3] as the final answer.

Answer 24

can i have the answer of question 3?

Answer 25

i meant c part

Answer 26

yea, :[x,y,z]=[0,0,-3]+t[-3,0-3]

Answer 27

@OsmondF

Answer 28

I am not sure on Part c sorry.

Answer 29

Ok, thanks anyway :)