CBSE Class 12-science Answered
Introduction to vector addition in a plane:
Vectors are physical quantities that are completely described by their magnitude and direction in space.
If there are two vectors and , their sum can be calculated by the triangle method as follows:-
Explanation to Vector Addition in a Plane
In the above diagram, we first draw vector , and draw from the arrow head of . The third side of the triangle is completed by the vector v, which represents the sum of vectors and .
Thus the sum of two vectors is defined as:
Vector Addition Formula for Vector Addition in a Plane
Force is a vector quantity. Let there be two force vectors and , acting on the same object. The object is set in motion under the action of the two forces and . Thus, on the combined action of and a third force is produced and it seems as if the object is set in motion under the effect of this single force . In fact, is the sum of the two force vectors and , that is,
Now, if the forces and are not applied in the same direction, and they are applied with an angle of 30 degrees to each other, the situation will be represented by the following diagram:
In the above diagram, to find the value of , we cannot simply add and . This is because and are not acting in the same direction, and thus their sum will depend on the angle between and .
Similarly, the resultant of all vector quantities is dependent on the angle between them.
Thus, to add two vectors, we need to take into consideration the angle between the two vectors. Let the angle between two vectors and be . The sum of the two vectors, is given by