# Vector Details with Diagram (Part 2)

# (The First Part of this post is here)

## Vector Details with Diagram (Part 2)

*Law of Parallelogram of vectors**:*

“If a particle simultaneously possesses two vectors represented in magnitudes and direction by the two adjacent sides of a parallelogram drawn from a point, their resultant is represented in magnitude and direction by the diagonal of the parallelogram passing through that point.”

*Resultant:*

origin O with angle α, R is the resultant acting along OB with an angle P from B. The perpendicular BN is drawn on Produce OA. Therefore, form the right angled triangle OBN, We get, OB^{2 }= ON^{2}+ BN^{2} Or, OB^{2 }= (OA+AN)^{2 }+BN^{2} Or, OB^{2 }= OA^{2 }+2OA .AN+AN^{2 }+BN^{2} Or, OB^{2 }= OA^{2 }+(AN^{2 }+BN^{2})+2OA .AN

*Direction Resultant:*

angle triangle, OBN, we get,

No. (1) equation is resultant of the vector and No (2) equation is Direction of the resultant.

*Vector Details* with Diagram (Part 2)

*The maximum and minimum magnitude of the resultant of two vectors acting at a point is equal to the sum and difference of their magnitude Or The resultant of two vectors acting at a point at same time can never be greater than to their sum and can never smaller than to their subtraction.*

Let the two vectors are P and Q and the angle between them is α. Therefore, the law of parallelogram, we know,

So that the maximum and minimum magnitude of the resultant of two vectors acting at a point is equal to the sum and difference of their magnitude, Or The resultant of two vectors acting at a point at same time can never be greater than to their sum and can never smaller than to their subtraction.

### Vector Details with Diagram (Part 2)

*Law of Triangle of vector:*

“If a body simultaneously possesses three vectors represented in magnitudes and directions by the sides of a triangle taken in order, the resultant is zero i.e. the body remains at rest. “Let P Q and R be represented by the three sides of triangle AB , BC and CA respectively. According to vector addition,

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#### Vector Details with Diagram (Part 2)

**Vector Details** with Diagram (Part 1)

Vector Details with Diagram (Part 3)

Vector Details with Diagram (Part 2)