Answer:
1) N.N , 2) N.Ne, SE.S, 3) N.E and 4) N.S
Explanation:
The cardinal points can in fact be worked as a Cartesian coordinate system (xy), so the relationships for the scalar product (dot product) are valid for both
A . B = A B cos θ
Where the bold in A and B indicate vectors, the values on the right are the modules of (A, B) and θ is the angle between the two vectors.
Let's make the products that are requested.
a) N. N the angle between the two vectors is zero and cos 0 = 1, the result the product squared
N.N = N N cos 0
º
N.N = N² 1
If N is a unit vector, module equal to one (1), N² = N = 1
N.N = 1
b) N. NE. The North-East are 45º with respect to the north, so the angle between the two vectors is 45º
N.NE = N Ne cos 45
N. NE = N Ne 0.707
If N and Ne are unitary
N. NE = 0.707
c) N. S these two vectors are on the same vertical line one up (N) and gold down (S), so the angle is 180º
N.S = N S cos 180
N.S = -1
d) N.E one goes up and the other to the right, the angle between the 90º doses
N.E = N E cos 90
N.E = 0
e) SE.S one of these vectors is 45º in the fourth quadrant (where x is positive and y is negative) and the other points vertically downwards (S) the angle between the two is 45º
In general, for these products the angle is measured from the positive part of the x-axis (EAST), therefore, 270º must be added to the Angle found
SE. S = Se S cos (270 + 45)
SE.S = 0.707
Order products from highest to lowest
1 N.N
2 N.Ne
SE.S
3 N.E
4 N.S
The N.NE and SE products. has the same numerical value, but one is in the first quadrant and the other in fourth quadrant
