Answer and prove you know many things?

Question

We all know that, in cross product(vectors) we use "sine" and in scalar product(vectors) we use "cosine".My question is why use
"sine" in cross product or dot product and why we use "cosine" in scalar product?What's the mystery?tell me in details.

Answer 1

This is difficult to describe succinctly in words. Vector diagrams in Cartesian 3-space make it immediately obvious.

Look at this:
http://cnx.org/content/m13603/latest/

Answer 2

What's so mysterious about a definition?
In fact both "dot" and "cross" products are "half truths" from the point of view of Grassman/Clifford/Exterior algebras.
If you think geometrically then the dot product gives you the projection of two vectors, while the cross product is the volume enclosed by the triad of vectors a = bxc. The first will involve a cosine and the latter a sinus.

Answer 3

It's all based on how they are defined.

Read up these pages:

http://en.wikipedia.org/wiki/Dot_product
http://en.wikipedia.org/wiki/Cross_product

and hopefully wyou'll understand.

The cross product of the two vectors a and b is denoted by a × b (in longhand some mathematicians write a∧b to avoid confusion with the letter x - this should not be confused with the logical "and" operator, ). It is defined as the vector which is perpendicular to both a and b with a magnitude equal to the area of the parallelogram they span.

The dot product of two vectors (from an orthonormal vector space) a = [a1, a2, … , an] and b = [b1, b2, … , bn] is by definition:
a1b1+a2b2+...anbn.

Answer 4

because when u draw a graph u will know why we will use that rules.if u want in detail i can explain nicely by drawing graphs and other things in a paper but in this way i cant help u out.sorry

Answer 5

LOL

Stuck doing your homework huh?

Answer 6

Well its like this, Oh I can't be bothered

Answer 7

are u sure u realy wanna know?