Displacement Math Example 2

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Example 2

medium
A robot moves from point A(1,2)A(1, 2) to point B(4,6)B(4, 6). Find the displacement vector and its magnitude.

Solution

  1. 1
    Step 1: Displacement vector d⃗=B−A=(4−1, 6−2)=(3,4)\vec{d} = B - A = (4-1,\ 6-2) = (3, 4).
  2. 2
    Step 2: Magnitude ∣d⃗∣=32+42=25=5|\vec{d}| = \sqrt{3^2 + 4^2} = \sqrt{25} = 5.
  3. 3
    Step 3: The robot moved 5 units in the direction of vector (3,4)(3, 4).

Answer

Displacement vector (3,4)(3, 4); magnitude =5= 5 units.
The displacement vector from A to B is found by subtracting coordinates of A from B. Its magnitude is the straight-line distance between A and B (computed via the distance formula). The direction is given by the angle of the displacement vector.

About Displacement

The straight-line change in position from start to end, with both a distance and a direction.

Learn more about Displacement →

More Displacement Examples

Example 1 easy

A person walks 5 m east and then 5 m west. What is their displacement?

Example 3 easy

A car drives 3 km north, then 4 km east. What is the magnitude of the total displacement?

Example 4 hard

A particle undergoes three displacements: [formula], [formula], [formula]. Find the net displacement

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