Warm Up Mar. 14th 1. Find the magnitude and direction of a vector

with initial point (-5, 7) and terminal point (-1, -3)

2. Find, in simplest form, the unit vector in the direction 4i – 2j

3. If r = <-3, 1> and u = <-1, 4>find y if 2r – 5y = u

4. Given v of magnitude 200 and direction 215°, and w of magnitude 150 in direction 162°, find v + w.

Homework Questions??

2D Vectors – Day 2

Dot Product, Angles Between Vectors &

Perpendicular Vectors

The Dot Product(also called scalar product)

<a, b>•<c, d> = ac + bd

Unlike addition and scalar multiplication with vectors, the dot product of vectors

is a scalar.

Find the dot product of the vectors

1. <1, -2>•<4, -3>

2.

3. (3i – j)•(3i – j)

10

5

1

2

Let v = <-2, 5>, u = <3, 4> and w = <-2, 1>.

Find the indicated quantity.

1. (u•v)w

2. u•2v

The angle, θ, between two vectors, u and v.

vu

vu cos

Find u•v, where θ is the angle between u and v.

1. |u| = 8, |v| = 10, θ = 150°

2. |u| = 2, |v| = 3, θ = 60°

3. |u| = 4, |v| = 1, θ = 90°

Find the angle between the vectors.

1. <-2, 5> and <3, -4>

2. <3, 2> and <6, 1>

3. <4, 3> and <-6, 8>

If the angle between two vectors is 90°, the vectors

are orthogonal or perpendicular.

Think About It…

What is true about the angle between two nonzero vectors u and v, if the following are true?

u•v = 0u•v < 0u•v > 0v = ku, where k is a scalar

Find the measure of angle ABC for A(2, -1), B(3, 4) and C(-1, 3)

Use vectors to determine whether ΔPAR with P(2, -2), A(5, 7) and R(-

1, -1) is right, acute or obtuse.

Find the measure of the angle between the lines 2x + y = 5 and

3x – 2y = 8.