Vectors And Vectoe Proofs

Question 1

What are vectors

Answer 1

Quantities with magnitude and direction

A line can be a vector as it has a length and a direction between two points

Question 2

How do we write a vecor on the line AB

Answer 2

→
AB

The arrow shows the direction between the two points

Question 3

If you had a triangle OBA
With length → OA being a and length → OB being b, in germs of a and b what is line AB

Answer 3

To find →AB we need to travel from A to B using the lines with measurements we know

To do this we travel backwards along line →OA , this gives us -a

Next we need to travel up to point B, from point O
Therefore we travel along the line →OB, giving us positive B

Therefore line AB = -a+b (or b-a)

This tells us how to move up and down the unknown linw

Question 4

Using the same triangle OBA how can we find the vector of line OP, when AP : BP is 3:1

(→AB = b-a)

Answer 4

3+1 = 4

→AP = 3/4

Therefore
→ AP = 3/4(b-a)
= 3/4b-3/4

Using →OA and → AP
We know →OP = →OA + →AP

→OP = a+ 3/4b + 3/4a
→ OP = 4/4a+3/4-3/4a
=1/4a+3/4b

Always factorise so

1/4(a+3b)

Question 5

If a point is on the midpoint of a line what is the lines ratio

Answer 5

1:1
So 1/2 : 1/2

Question 6

How do we know which line to move up and down?

Answer 6

It is the line with no vectors on it - so we must find the vector