1. ## New to vectors

Hey guys, I'm in year 9 and our teacher gave us some extension work and it's on vectors which we've never done before. These questions are probably really basic but it would be great if you could give me a hand with them

2. Given the vector (-5,12) find the following vectors:

a) same direction, twice as long
b)same direction, length 1
c) opposite direction, length 10
d) opposite direction, length c

Im really lost on the above ones

4. Find the lengths of the following vectors:
a) (3,4)
From what i've tried to read on wiki the answer to this is 5 (pythagoras)
b) 1998(3,4)
I don't understand what a number in front means
c) 1998/5 (3,4)
d) t(3,4)

Thanks heaps guys

2. Originally Posted by IndoorKid
2. Given the vector (-5,12) find the following vectors:
a) same direction, twice as long
b)same direction, length 1
c) opposite direction, length 10
d) opposite direction, length c
The vector $\displaystyle \left\langle { - 5,12} \right\rangle$ has length $\displaystyle \left\| {\left\langle { - 5,12} \right\rangle } \right\| = \sqrt {( - 5)^2 + \left( {12} \right)^2 } = 13$

What are the lengths of $\displaystyle \left\langle { - 10,24} \right\rangle \;\& \;\left\langle {\frac{{ - 5}}{{13}},\frac{{12}}{{13}}} \right\rangle$?

Why is the vector $\displaystyle \left\langle {50, - 120} \right\rangle$ oppsite in direction to the given vector?
What is its length?

3. Originally Posted by IndoorKid
4. Find the lengths of the following vectors:
a) (3,4)
From what i've tried to read on wiki the answer to this is 5 (pythagoras)
b) 1998(3,4)
I don't understand what a number in front means
c) 1998/5 (3,4)
d) t(3,4)

Thanks heaps guys
* Draw a picture of co-ordinate axes and locate the point. This will help you see why pythogorus theorem is applied.

* t(3,4) is a notation for (3t,4t). For example 6(3,4) = (18,24)

Use the above suggestions to solve the problem. Do post your attempts