One Order of Magnitude

Introduction about one order of magnitude

       This article is about one order of magnitude. One order of magnitude is nothing but it is a one dimensional magnitude.The tutor from the tutor vista help the students in online to find one order of magnitude. This is nothing but about the one dimensional vector. One order of magnitude is explained with the tutors from the tutor vista website. The tutors are highly eduacted to guide the students in online. They help more in one order of magnitude. Below we can see one order of magnitude.

One Order of Magnitude

This arrow marks shows the model representation of one dimensional vectors.

One dimensional vector

The vector A and D are same with the up direction and magnitude of 4. So vector A and D are meaned as equivalent vectors.

The vector B has magnitude of 2 in the up direction

The vector C has the right direction with magnitude of 4

OP-one dimensional vector

This vector is represented with two points. The first point is O and it is called the starting point of the vector and the second point is P and it is called as ending point.

Magnitude of a vector

The magnitude of vector is mentioned with modulus symbol. Example |OP|

Vectors in opposite direction

BOA-one dimensional vector

This is the simple representation of vectors in both direction. OA is the normal vector representation and OB is the opposite vector representation of OA. Here O is the centre.

Zero vector

The magnitude of zero vector is zero |0|

Unit vector

The unit vector is nothing but the length of 1 unit in any direction.

One Order of Magnitude

Magnitude of cross product

vector

`vecu = (u_x, u_y, u_z)` and `vecv = (v_x, v_y, v_z)`

The cross product is defined as

`U xx V = hatx(u_y v_z - u_z v_y) - haty (u_x v_z - u_z v_x)+ hatz ( u_x v_y - u_y v_x)` ------------------(1)

          `= hatx(u_y v_z - u_z v_y) + haty (u_z v_x - u_x v_z)+ hatz ( u_x v_y - u_y v_x)`   ------------------(2)

`u xx v =|[hatx, haty, hatz],[ u_x, u_y, u_z],[ v_x, v_y, v_z]|` --------------------------------------------------------(3)

Here `hatx, haty, hatz ` are unit vectors.

uxv is always a perpendicular to both u and v

In case of a two dimensional vector, the cross product of two vectors a and b is a third vector. The magnitude of the vector product is

|c| = |axb| = `ab sin theta`

Here theta is the smaller of the angles between the two vectors.

One Order of Magnitude

Problem 1: Find the magnitude of `2 veci - vecj + 7 veck`

Solution:

Magnitude of `2veci - 3vecj + 7 veck = |2veci - 3vecj + 7 veck|`

                                                   = `sqrt((2)^2 + (-3)^2 + (7)^2)`

                                                   `sqrt(4+9+49)`

                                                  =`sqrt (62)`
 
 
 

Problem 2: Find a unit vector in the direction of the vector `veca = veci+2vecj+3veck`

Solution

`veca = veci + 2vecj + 3 veck`

Magnitude =` |veca| = sqrt (1^2 +2^2 + 3^2 )`

                = `sqrt14`

unit vector in the direction of veca is given by

`hata`  =` (veca)/|veca|`

      = `(veci + 2vecj + 3 veck)/sqrt14`

      = `(1/sqrt14 veci + 2/sqrt (14) vecj + 3/sqrt (14) veck)`

Problem 2: Find the magnitude in the direction of the vector `veca = 3veci+4vecj+1veck`

Solution

`veca = 3veci + 4vecj + 4+ veck`

Magnitude =` |veca| = sqrt (3^2 +4^2 + 1^2 )``sqrt (9 + 16 + 1`

                = `sqrt 26`