Why do I need to know how to multiply vectors?

Question

Adding is one thing, but what's the point of multiplying them?

Answer 1

Because there are quite a few quantities in physics which are found by vector multiplication.

One example is the quantity "Work"; which is usually defined as Force × distance. However, "Force" and "Distance" are actually both vectors; and to get the proper value for "Work", you need to take into account the _directions_ of the force and the distance, not just their magnitudes. The correct way to multiply these is to use the so-called "vector dot-product." In a nutshell, that means you multiply the magnitude of the force vector, times the magnitude of the distance vector, times the cosine of the angle between them.

There are actually two ways to multiply vectors; one is called the "dot-product" as described above; the other is called the "cross-product" and uses a different formula. Whether or not you use the "dot-product" or the "cross-product" depends on the application.

Answer 2

Would you like to know how much of the sun's energy falls on 1 square meter of a planetary probe's solar panel when the sun is at an angle of 37 degrees? Then you need to know how to multiply vectors.

Would you like to study the swirling aerodynamics of storms on other planets? Then you need to know how to multiply vectors.

Answer 3

there are two important types of vector multiplication that you encounter in physics.

One is called the dot product; geometrically, this tells you the product of the magnitude of the two vectors times the cos of the angle between them; it is useful in calculating things like work and flow through surfaces

Another is the cross product, which is used to find torques and forces on charged particles in magnetic fields.

This is a very quick overview of the power of these types of vector multiplication operations.

Answer 4

You don't need to. There are tons of people in low paying jobs who don't know how to do it.

But seriously... if you know how to, you can determine the angle between the two vectors. That's very useful in geometry and you need it basically everywhere in mechanical engineering.

In physics the multiplication of vectors is essential to e.g. calculate the work a force can perform. In EE one can calculate electrical power in AC circuits where voltage and current are out of phase. And loads of other stuff.

:-)

Answer 5

Because in two or more dimensions there will be angles involved, and you can't just add the quantities of these angles.

Answer 6

Because if you knew that, it would be easy for you to make electric power meter to spin in the other direction.
And save tons of money.