Physical meaning of a×b cos(θ) and how to represent it

[asrith926]

So, the other day, I was learning about Scalars and Vectors and about Dot product and Cross Product. Now, in Cross Product, I was just thinking, when my thought slipped on the following stone:
What is the physical implication of => aXb(cos$$\vartheta$$) ?
I mean, how would you represent it on a paper?

 

[Andrew Mason]

So, the other day, I was learning about Scalars and Vectors and about Dot product and Cross Product. Now, in Cross Product, I was just thinking, when my thought slipped on the following stone:
What is the physical implication of => aXb(cos$$\vartheta$$) ?
I mean, how would you represent it on a paper?

Its magnitude is the projection of a onto the unit vector in the direction perpendicular to the b direction (in the plane made by a and b) multiplied by the magnitude of b. Its direction is perpendicular to the plane made by a and b.

It is defined that way because it is useful. A number of phenomena in physics have relationships that depend on component of a force or velocity perpendicular to a radial vector and proportional to the magnitude of that radius: eg. angular momentum, torque, Lorentz force.

AM

 

[Studiot]

What is the physical implication of => aXb(cos)

I'm sorry could you elaborate on this further?

What is the angle you are talking about?