(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, OB² = ON²+ BN² Or, OB² = (OA+AN)² +BN² Or, OB² = OA² +2OA .AN+AN² +BN² Or, OB² = OA² +(AN² +BN²)+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)