Given a real number (scalar) r and a vector a=(a_1, a_2), we define a new vector r a (or r*a or a multiplied by r) by
- r a=r (a_1,a_2)=(r*a_1, r*a_2) (multiply with r inside the parenthesis).
- 3 (1.1, 2.3) = (3*1.1, 3*2.3)=(3.3, 6.9).
We say that ra is obtained by multiplying the vector a=(a_1, a_2) by the real number r and call this operation multiplication of a vector by a scalar.
Below we will meet other types of multiplication connected with scalar product of vectors and vector product of vectors, both being different from multiplication of a vector by a scalar.
We define for vectors a and b
- -a = (-1)a = (-a_1, -a_2)
- a – b = a + (-b) .
The sum 0.7a-b of the multiples 0.7a and (-1)b of the vectors a and b.