Warm UpMar. 14 th 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.

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Presentation transcript:

Warm UpMar. 14 th 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 = and u = 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) = ac + bd Unlike addition and scalar multiplication with vectors, the dot product of vectors is a scalar.

Find the dot product of the vectors (3i – j)(3i – j)

Let v =, u = and w =. Find the indicated quantity. 1. (uv)w 2. u2v

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

Find uv, 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. and 2. and 3. and

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? uv = 0 uv < 0 uv > 0 v = 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.