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.

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: