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Addition of Vectors
Addition of Vectors Let two vectors, a and b , be defined as follows: a = <a_1, a_2, ..., a_n>} and b = <b_1, b_2, ..., b_n> Then the sum of...
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Addition of Vectors Let two vectors, a and b , be defined as follows: a = <a_1, a_2, ..., a_n>} and b = <b_1, b_2, ..., b_n> Then the sum of...
Let two vectors, a and b, be defined as follows:
a = <a_1, a_2, ..., a_n>} and b = <b_1, b_2, ..., b_n>
Then the sum of the vectors, denoted by a + b, is a new vector containing the components:
a + b = <a_1 + b_1, a_2 + b_2, ..., a_n + b_n>
Geometric Interpretation:
The addition of vectors represents adding the corresponding components of the vectors. For example, if **a = <1, 3, 5>` and b = <2, 4, 6>, then a + b = <3, 7, 11>.
Examples:
**Add the vectors **<1, 2, 3> and **<4, 5, 6>**: **<5, 7, 9>
**Add the vectors **<2, 4, 6> and **<3, 6, 9>**: **<5, 10, 15>
**Add the vectors **<a, b, c> and **<d, e, f>**: **<a + d, b + e, c + f>
Properties of Addition:
(a + b) + c = a + (b + c)
(a + b) - c = a - (b - c)
a + b = b + a
The addition of vectors is a linear operation, meaning that the order in which the vectors are added does not affect the result