Vector Intuition Math Example 1

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

Example 1

easy
A displacement vector points 3 units east and 4 units north. What is the magnitude of this vector?

Solution

  1. 1
    Step 1: Represent the vector as v⃗=(3,4)\vec{v} = (3, 4).
  2. 2
    Step 2: Magnitude ∣v⃗∣=32+42=9+16=25=5|\vec{v}| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5.
  3. 3
    Step 3: The vector has magnitude 5 units.

Answer

∣v⃗∣=5|\vec{v}| = 5 units
A vector has both magnitude (size) and direction. The magnitude is its length, computed using the Pythagorean theorem in 2D. A 3-4-5 right triangle gives a magnitude of 5 — the actual straight-line distance of the displacement.

About Vector Intuition

A mathematical object with both a magnitude (size) and a direction, often drawn as an arrow.

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More Vector Intuition Examples

Example 2 medium

Vectors [formula] and [formula]. Find [formula] and interpret the result geometrically.

Example 3 easy

What is the difference between a vector and a scalar? Give one example of each.

Example 4 hard

Find the unit vector in the direction of [formula].

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