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Vector Subtraction Examples B + ( − A ) = ( 5 , 9 ) + ( − 1 ) ⋅ ( 3 , 6 ) B − A = ( 5 , 9 ) + ( − 3 , − 6 ) B − A = ( 5 − 3 , 9 − 6 ) B − A = ( 2 , 3 )

To find vector , the point A is the terminal point and point B is the starting point. The directional vector can be determined by subtracting the start from the terminal point.

The unit vectors of a vector are directed along the axes. In the 3-d plane, the vector v will be identified by three perpendicular axes (x, y, and z-axis). In mathematical notations, the unit vector along the x-axis is represented by i.

Vector subtraction is done in the same way as vector addition with one small change. We add the first vector to the negative of the vector that needs to be subtracted. A negative vector has the same magnitude as the original vector, but points in the opposite direction (as shown in Figure 5.6).

Subtracting the vector B from the vector A, which is written as A − B, is the same as A + (−B). Since it does not matter in what order vectors are added, A − B is also equal to (−B) + A. This is true for scalars as well as vectors. For example, 5 – 2 = 5 + (−2) = (−2) + 5.

A unit vector is a vector that has a magnitude of one and has a length of one. If, for example, the vector v = (1, 3) is not a unit vector because the magnitude of the vector is not equal to 1, then the vector is not a unit vector. For example, |v| = (12+32) ≠1 is not a unit vector.

The vector subtraction of two vectors a and b is represented by a - b and it is nothing but adding the negative of vector b to the vector a. i.e., a - b = a + (-b). Thus, subtraction of vectors involves the addition of vectors and the negative of a vector. The result of vector subtraction is again a vector.