Vector in a Coordinate Plane

Theory

Vectors are quantities that have both magnitude and direction.

They can be represented in a coordinate plane as arrows pointing from one point to another.

A vector in a 2D coordinate plane can be represented as v=v1,v2\mathbf{v} = \langle v_1, v_2 \rangle, where v1v_1 and v2v_2 are the components of the vector along the x-axis and y-axis, respectively.

Exercises

Exercise 1
Question

Calculate the magnitude of the vector v=3,4\mathbf{v} = \langle 3, 4 \rangle.

Show solution ↓
Solution
v=32+42=5\|\mathbf{v}\| = \sqrt{3^2 + 4^2} = 5