## May 26, 2020

### VECTORS – 4 (MASTER ADVANCED PHYSICS)

(FOR ALL TOP EXAMS)

VECTORS – 4

RESOLUTION OF VECTORS

It is a good idea to break one vector into what is called rectangular components.

What does this mean?

Suppose you have a 2 dimensional vector and we want to have 2 one dimensional vectors, one on the x axis and the other on the y axis.

These two one dimensional vectors sum up and give the original vector.

So, if we have a vector of 10 units and at 60 degrees to the X axis, then

The component on the X axis is A Cos (theta) and the component of the Y axis is A Sin (theta)

Let us check whether this is true.

WE have seen that R2 = a 2 + b2 + 2ab Cos(theta)= a sin2 (theta) + BCos2(theta) + 2ab Cos(theta)

= 10(Sin2(theta) + Cos2(theta) ) + 0 (as Cos 90 is zero

= 10 which is true...

So, we can break a vector into two components along X axis and along Y axis.

If we have say 10 forces acting on a body, and if we break EACH one into components in X axis and y axis, then finally we will have

10 vectors along x axis

10 vectors along y axis.

Each can be added very simply. As it is one dimensional.

And finally we will have after adding, ONE value of the vector along x axis A and one along y axis B.

So, resultant can be got by

R2 = A2 + B2

R = root of a2 + b2

The final angle would be Tan b/a where b= Y component and a= X component.

So these are the basic concepts and also formulae.

PRODUCT OF VECTORS

Dot product – A DOT B = AB COS (THETA)

Cross product – A CROSS B = AB SIN (THETA)

We will see these concepts by linking to physics in later chapters.