Name: Magnitude of a vector: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 37 s
Description: What is the magnitude (length) of the vector v = ⟨ 6, -2 ⟩? Try it, then watch the animated solution.

The magnitude of a vector is the length of its arrow. Draw

\langle 6, {-2} \rangle

:

6

right and

2

down.

The components are the legs of a right triangle:

6

across and

2

down. The arrow is the hypotenuse.

Pythagorean theorem:

|\mathbf{v}|^2 = 6^2 + ({-2})^2 = 36 + 4 = 40

.

Take the square root:

|\mathbf{v}| = \sqrt{40} = \sqrt{4 \cdot 10} = 2\sqrt{10}

.

Traps:

40

skips the square root,

8

adds the legs, and

4\sqrt{2}

squares

{-2}

to get

{-4}

.

Try it first