Vectors show up on the ACT as 1-2 questions per test. They are not on the SAT. The concepts are straightforward if you think of vectors as arrows with coordinates.

What Is a Vector?

A vector has both magnitude (length) and direction. Written as where is the horizontal component and is the vertical component.

Think of it as: "Go right units and up units."

Vector Operations

Addition — add component by component:

Subtraction — subtract component by component:

Scalar multiplication — multiply each component:

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Magnitude (Length)

The magnitude of is:

This is just the Pythagorean theorem!

Example:

Recognize the triple — it saves time.

Vector from Two Points

The vector from point to point is:

Example: Vector from to :

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Common Mistakes to Avoid

  • Confusing points and vectors: A point is a location. A vector is a displacement. They look similar but mean different things.
  • Wrong subtraction order: goes FROM TO : subtract from , not the other way around.
  • Forgetting to square root: Magnitude involves , not .

ACT Pro Tip

Vector questions on the ACT are almost always about component-wise arithmetic or finding magnitude. Treat the and components as two separate, independent calculations. If you can add two numbers, you can add two vectors.

Practice vectors with our Vectors lesson — ACT-exclusive content.