Vector is important to learn physics
now unit vector along x axis is i cap ( cap = ^)
unit vector along y axis is j cap
unit vector along z axis is k cap
what is advantage of writing this vector in i,j,k form it makes operation of vector easy addition, subtraction, multiplication and division with similar quantity i,j,k this is main advantage .
with the help of unit vector we can find position of any point in space or 3-D easily following the root of x, y, z axis hence any point suppose p(2,3,5) located in space then we can write this position vector in unit vector form suppose o is origin o(0,0,0)
op = r = (2-0)i^ +(3-0)j^+(5-0)k^
r = 2i^+3j^+5k^
where r is full vector and i^, j^, k^ are unit vector similarly any other point can be written as
r₁ = 2i^+3j^-5k^, r₂ = 2i^-2j^-3k^ now here it is easy to make operation between r,r₁,r₂ vector without using unit vector it was difficult to make operation between r,r₁,r₂ now this can be any vector quantity like displacement, velocity, acceleration, force .
now for magnitude calculation for such type of unit vector
suppose r = ai^+bj^+ck^ then its magnitude will be written as
|r| = ⎷a²+b²+c² under root square of the a,b,c
Equal vector condition:
Two vector are called equal if and only if having equal magnitude and same direction .
→ here A vector and B vector are equal
Negative vector: having equal magnitude in opposite direction
Col linear vector : vector having same direction but different magnitude
Co planer Vector : vector in same plane having different magnitude and direction
A →→→→→→ B
Null Vector or Zero Vector: Vector having Zero magnitude but having direction a point is a null vector or zero vector here its magnitude is zero then what is direction answer is any direction a point has any direction simply add two opposite vector what will be result its magnitude will be zero null since it is a vector addition hence result will be also a vector pointing towards any direction.
addition and subtraction of null vector with other vector not effect vector but multiplication becomes zero.
Important : what is difference between A and |A| here simple A indicate that quantity is scalar only magnitude but |A| indicates it is a vector quantity but we are only interested for magnitude this is the difference . there all vector having great application in whole physics we will study latter where vector concept will be very important so focus ton command over vector and be yourself as vector direction to reach your destination.
thanks for learning Vector is important to learn physics
dated 26th May 2018