Arithmetic Operations on Vector Quantities 1

 

                                Vectors 


Vectors tell us the distance of a point in a graph from the origin. Vectors are made up of two numbers written vertically between a set of brackets. 



Here, x and y are two numbers. X represents how much a point has moved along the x axis, horizontally. And y represents how much that point has moved up, vertically. If x or y are negative, it means that the point has shifted left or down respectively. Basically, the coordinates of the point!


We can use this to solve various questions for example;
if we need to find the distance of a point from its origin or multiply the vectors of two points or add them, out of other operations.


Distance:
To find the distance of a point from its origin we simply use the Pythagoras's theorem. 

We know that the point has shifted horizontally by x and vertically by y, from the origin. The distance therefore is the hypotenuse! 

All we do is:
1. Square both x and y and add them.
2. Find the square root of the sum.
3. This will be your distance!



Addition:
Adding up two vectors is really simple. All you do is add their 'x' values and then add their 'y' values and write the new 'x' and y values vertically, forming a new vector. 






For multiplication, one uses the same concept by multiplying the x and y values to form a new vector.


Questions:

1.

Solution:


2.



Solution:



 



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