If two vectors are having equal
magnitude and certain angle between them , we can find the resultant of the two
vectors using the parallelogram law as shown. Using the same concept it can be
proved that, if the resultant of two equal and vectors is equal to any one of
the vectors then the angle between them is 120°.

**Vectors subtraction**is similar to that of the vector addition the only differences will be getting an extra negative sign. We can solve all the problems of vectors subtraction using the same concepts of vector addition. All rules like parallelogram law and triangular law can be applied to this concept by taking care of proper signs.

**Problem**

Let us consider a circular disc
of radius R and it is having a translator motion.Find the magnitude and displacement of
completion of the have the revolution. Also find the angle made by the
resultant.

**Lamis Theorem:**

This theorem helps in solving
some problems vectors. The concept of the theorem and application is solved as
explained below. As per this concept, if the vectors are acting and the is in equilibrium, the ratio of the vectors and its opposite

**sin**angle is always constant.
The problem is solved here
actually can be solved even with the concept of resolution vectors.

**Application of triangular law:**

Determination of an external
force applied horizontally on the Bob so that the pendulum gets a vertical
displacement

Let us consider spherical body
having mass m attached to a string of length l two a rigid support as shown.
Letters apply a horizontal for F on the spherical body so that it displaces an
angle with the vertical. At the instant the spherical body is in a equilibrium
position just because there are three forces acting on it as shown.

By resolving the tension into components we can write a equilibrium equations as shown. Here we can calculate force as well as the tension in terms of the weight of the body.

By resolving the tension into components we can write a equilibrium equations as shown. Here we can calculate force as well as the tension in terms of the weight of the body.

**Problem:**

Let us consider two vectors x and square root of 2 are having some angle
between them. Let the resultant of the two vectors is square root of six and is perpendicular to
the vector X . Then find the value of the x and also find the angle between the
two vectors ?

In solving this problem we need
to take parallelogram law vectors into consideration. It is considered the two
vectors is the two sides of the parallelogram. As the resultant is
perpendicular to the X the angle between the two vectors shall be more than
90°. The solution is as presented below.

Let us considers another problem. Let a person is
walking 10 m east, then 10 m north and then 10 root 2 m Southwest. Find his
final displacement.

In solving this problem we have
to treat each of the position as vector. I J and K are the unit vectors along
the x-axis y-axis and z-axis . They
choose the direction of the vector. Each vector is represented and the third
vector resolved into components as shown. The resultant of all the vectors is
simply the vector sum of all of them.

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hello sir..i m sujata. thank u so much for providing ur handwritten notes..they r amazing...i hav a problem..can u plz tell me that if one of the vector and the resultant is given then how to calculate the 2nd vector..and also the angle?

ReplyDeleteGood very useful

ReplyDeletethank u so much providing this handwritten notes

ReplyDeletethank u so much providing handwritten notes

ReplyDelete