Vectors help?

[Andiio]

For the following pairs of vectors, calculate the magnitude and direction of vector a + vector b and vector a - vector b.

a) vector a = 10km north and b = 6km north-east
f) vector a = 50 unites in a direction 300 degrees T and vector b = 40 units in a direction 30 degrees T

there are others and I can kind of do them, but am not sure which method I should use.

Method 1 - Constructing a triangle, figuring out vector values with sine/cos rules.

Methods 2 - Change the vectors into coordinates (horizontal, vertical), i.e. for a),

Vector a would be - (0, 10)
and Vector b would be - (x, y)
When you construct a triangle and use pythagoras/simple trig to figure out the other sides;
Hence you would get vector b(4.24, 4.24)

Then you just add these 2 vectors together and use the magnitude/direction rules. [ (a,b) = sqrt(a^2+b^2)]

How would you guys do it? :/

[TrueTears]

a)

Let the unit vector pointing north be and the unit vector pointing east be





Now add.

[Andiio]

a)

Let the unit vector pointing north be and the unit vector pointing east be





Now add.

I haven't learnt i and j notation yet though :S
It's the next chapter, so i'm just wondering how you would do it without that notation?
Would there be questions like the above in Spesh where you would have to work it out with these methods?

Thanks in advance!