8-1 Geometric Vectors 8-2 Algebraic Vectors

Vectors- a ray that displays direction and force (magnitude) Vectors can be written as 𝑎 𝑜𝑟 The magnitude of a vector is 𝑎

Scalar: Multiplies the magnitude of the vector ( does not change direction) Ex) 3𝑎 ⃑

Use a ruler and protractor or measure the magnitude and direction of 𝑛 (see worksheet) 2) Draw a vector that has magnitude 3.6cm and direction of 30°

You can add to vectors together to get a resultant.

3) Find the sum (resultant)

Hint: When subtracting a vector, add the “negative” in the opposite direction)

Although drawing vectors is an easy method, it is not always very accurate. Instead, we can use algebra. You can write vectors using the x and y coordinates. Just remember, vectors don’t always have to be in standard position

If you know the initial and terminate coordinates, you can rewrite the vector as the coordinate (x2-x1, y2-y1) You can use the Pythagorean theorem to find the magnitude of a vector.

You can add/subtract vectors by adding the x components and y components separately. Given, 𝑚 = 5,−7 𝑛 = 0,4 𝑝 = −1,3 6) 𝑚 + 𝑛 7) 𝑚 ⃑-𝑛 ⃑ 8) 7 𝑝 9) 2 𝑚 +3 𝑛 − 𝑝

Unit Vector: Has a magnitude of 1 When talking about unit vectors, we use 𝑖 to talk horizontal direction (x) and 𝑗 to talk about the vertical direction.

Any vector can be written in terms of 𝑖 𝑗