Understanding vectors and gibberish

[Venito]

Homework Statement

For the line y=2x+4

A, find the posiotion vector of the point A, on the line, Which is 6 units from the origin in the 1st quadrant. Express your answer in:

i.] Matrix form. [Never done matrix]

ii.] the form OA [Line with arrow pointing right above it.] = xi +yj

B, Find the position vector for the point B on the line, which is 12 units from the origin in the 3rd quadrant. Express your answer in,

i.] Matrix

ii.] the form OB [Line above it facing right.]

C, Find the cordinates of the mid point of AB.

d, what is the vector equation of the line y=2x+4 in parametric form?

The Attempt at a Solution

Now I know I am nearly 19. Finished school 2 years ago and am now working a 5am-5pm job manuel not pen pushing an just find it hard to study and remeber when I am working.
So forgive me for F%%$ing up.

Right apart from just drawing the graph of y=2x+4 that is all I get.
I think they are meaning to add a point 6 units from the 0 middle point on graph. But not sure.

Which would give me a rectangle. Point starting from -2,0 0,6 14,6. That is if I have done it right. I have done it x,y. That they right way around.

What on Earth do I do from here if I am right?

Cheers,

mac

 

[zachzach]

Homework Statement

For the line y=2x+4

A, find the posiotion vector of the point A, on the line, Which is 6 units from the origin in the 1st quadrant. Express your answer in:

i.] Matrix form. [Never done matrix]

ii.] the form OA [Line with arrow pointing right above it.] = xi +yj

B, Find the position vector for the point B on the line, which is 12 units from the origin in the 3rd quadrant. Express your answer in,

i.] Matrix

ii.] the form OB [Line above it facing right.]

C, Find the cordinates of the mid point of AB.

d, what is the vector equation of the line y=2x+4 in parametric form?

The Attempt at a Solution

Now I know I am nearly 19. Finished school 2 years ago and am now working a 5am-5pm job manuel not pen pushing an just find it hard to study and remeber when I am working.
So forgive me for F%%$ing up.

Right apart from just drawing the graph of y=2x+4 that is all I get.
I think they are meaning to add a point 6 units from the 0 middle point on graph. But not sure.

Which would give me a rectangle. Point starting from -2,0 0,6 14,6. That is if I have done it right. I have done it x,y. That they right way around.

What on Earth do I do from here if I am right?

Cheers,

mac

First off it might make it easier to graph y = 2x + 4.

A. 6 units is the distance from the origin (0,0) to the point. So if you drew a straight line from (0,0) to the point A the length of that would = 6. That distance can be found using the Pythagorean theorem. Just draw a dot at a random point in the first quadrant (top right) and draw a line from the origin to it. Then make a right triangle. You will see the sides of the triangle are of size x and y. Then use Pythagorean theorem to get the distance.

I think the two parts is just notation. The line above the OB means it is a vector $$\vec{OB}$$ Once you solve for x and y from Pythagorean put those into xi +yj and leave the i and j there. The i and j just mean they are vectors going in the x and y directions respectively. i stands for the x direction and j stands for the y direction. For matrix form either $$\left( \begin{array}{cc} x & y \end{array} \right) \left( \begin{array}{cc} x\\ y \end{array} \right)$$
either one for whatever your x and y values are.

 

[lanedance]

so let's start with A i.)

first, always start by drawing a picture

Now draw the line y=2x+4
Then draw a circle of radius 6, with centre (0,0)
You're looking for where the line and circle intersect.
There will be 2 intersection points.
The question asks for the first quandrant, that is just the upper right section of the coordinate axes where both x & y are positive.

You can solve for this by writing the equation of a circle of radius 6
$$x^2 + y^2 = 6^2$$

use the equation of a line to substitute in and solve for x or y
if you find the solution is:
x=a, y = b
i) then in matrix form it will be (a,b) (or vertically with a & b on top of each other)
ii) write the same numbers as ai+bj

 

[Venito]

Thank you all very much. That makes much clearer sence.

mac