Show that the "law of cosines" derives from finding the magnitude of the difference of two vectors. make a great drawing illustrating this! as a consequence, show that if the two vectors are orthogonal, the law of cosines reduces to the pythagorean theorem.

Let   be three vectors which represent sides of Triangle.

Using triangle law, that is for a closed path the sum of three vectors will be zero.

Which is Cosine law that is "Law of Cosines" for a Triangle.

If two vectors are Orthogonal, that is vector a and vector b, then their dot product will be Zero.

So, Law of Cosine Reduces to

Which is the Pythagorean Theorem, where a and b are smaller sides of triangle and,c,  is the Hypotenuse of Right Triangle.

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves