Vector Addition, Subtraction, and Scalar Multiplication Math Example 5

Follow the full solution, then compare it with the other examples linked below.

Example 5

medium
Find the vector from point A(1,3)A(1, 3) to point B(4,−1)B(4, -1).

Solution

  1. 1
    AB→=B−A=⟨4−1,−1−3⟩=⟨3,−4⟩\overrightarrow{AB} = B - A = \langle 4-1, -1-3 \rangle = \langle 3, -4 \rangle.
  2. 2
    This vector points from AA toward BB.

Answer

⟨3,−4⟩\langle 3, -4 \rangle
The vector from point AA to point BB is found by subtracting the coordinates: AB→=B−A\overrightarrow{AB} = B - A. This is one of the most common applications of vector subtraction.

About Vector Addition, Subtraction, and Scalar Multiplication

Vectors are added and subtracted component by component. Scalar multiplication multiplies each component of a vector by a number. If u=⟨u1,u2⟩\mathbf{u} = \langle u_1, u_2 \rangle and v=⟨v1,v2⟩\mathbf{v} = \langle v_1, v_2 \rangle, then u+v=⟨u1+v1,u2+v2⟩\mathbf{u} + \mathbf{v} = \langle u_1 + v_1, u_2 + v_2 \rangle and ku=⟨ku1,ku2⟩k\mathbf{u} = \langle ku_1, ku_2 \rangle.

Learn more about Vector Addition, Subtraction, and Scalar Multiplication →

More Vector Addition, Subtraction, and Scalar Multiplication Examples

Example 1 easy

If [formula] and [formula], find [formula].

Example 2 medium

Find [formula] where [formula] and [formula].

Example 3 medium

Given u = <2, -1> and v = <3, 5>, find 2u - v and its magnitude.

Example 4 easy

Compute [formula].

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