At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
you're answering to yourself?
dot product is a scalar quantity therefore applying product of two vectors in same direction will give scalar quantity, which is cos component of one in the direction of other, and reverse is in sin theta because it gives vector product
What that doesn't make any sense.. the real reason why there are two kinds of products of vectors is because in nature .. we have defined quantities such that in some two vectors when multiplied gives a scalar .. EG work = force times displacement.. since work has to be scalar.. we define scalar product.. at the same time.. torque is force times position vector.. has to be a vector.. hence we define vector product.. So the two kinds of products in vectors are actually defined cause we need them to explain the above examples.. !
try to understand not to manipulate things , read what i have written, first, now things are not vector or scalar in real life , secondly, you need to understand what does scalar and vector stands for , define use first not define objects by tools, show use of tools to define object , hope this time it will make sense to you, whatever you have written is magnification of rote learning not the visualization of concept behind it
vectors and scalars are obviously DEFINED by us.. to deal and work with physical quantities BETTER!! "dot product is a scalar quantity therefore applying product of two vectors in same direction will give scalar quantity" This statement makes no sense what so ever.. product of two vectors in same direction will give scalar?!??! what you mean to say is.. the scalar product is basically telling how much two vectors are parallel to each other.. and the vector product how much two vectors are perpendicular to each other!
no again i am sorry to say you didnt get what i wrote i tried to define mathematically why we take cos component in dot product , well keep up the good work by the way thanks :)
so you mean to say.. since dot product is to find how much parallel they are.. we need to take the cos component of a vector .. so that we get the parallel component of it :P
i said we take cos component because lets say if you are applying force of 10N on a block at an angle of 30 degrees then to find work we need to take dot product of it because that gives a scalar quantity and we take direction of motion in the direction of net force which makes the sense that you need to take cos component of force with the direction of motion, well it was nice to discuss i am off to bed now i am sorry its too late here : ):D
however.. what i am saying is.. its done the other way around :P.. dot product was not defined first.. we first define what work is .. and then since work is scalar and its a product of two vectors.. we then define what is called as the DOT product .. !!
cool, good night :)