Difference of vectors
- Author:
- Krishna Bahadur Bista
- Topic:
- Vectors
Definition: Let and be any two vectors. Then their difference, denoted by , is defined as = = . For example, (6,8)-(10,9) = (6-10,8-9) = (-4,-1)
and and
Properties of addition of vectors: (i) (commutative law)
(ii) (Associative law)
(iii) (Scalar multiplication distributes over the addition of vectors)
Multiplication of a vector by a scalar: Let be any vector and k be any scalar then . This shows that the scalar multiplies both x and y components of the vectors. For example, if then = (16,20). Similarly 4(5,9) = (20,36) etc.