12.7 Geometric Vectors. Vector: a quantity that has both magnitude and direction. A tail B head vectors can be placed anywhere on a grid, not necessarily.

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Presentation transcript:

12.7 Geometric Vectors

Vector: a quantity that has both magnitude and direction. A tail B head vectors can be placed anywhere on a grid, not necessarily starting at the origin Note: the textbook will use bold print v, we will write The magnitude or length or norm of a vector can be found using the Pythagorean Theorem Vectors are equivalent if they have the same magnitude and direction no matter where they are located.

If you add two vectors you get a resultant vector. There are two methods. Note: Subtracting vectors is like adding the opposite of the second vector. Ex 1) a)Find Tail-to-headParallelogram a)Find Tail-to-headParallelogram

Zero vector: If is the zero vector (magnitude = 0) A scalar will change the length of a vector. If a is a scalar and is a vector If a is negative, the direction reverses Ex 2) Use vector to draw & find the norm of

We can find the horizontal & vertical components of a vector using trig. θ y = rsinθ x = rcosθ Ex 3) Given that vector has a magnitude of 10 and direction of 135°, find the x & y components. 135° 10

Vectors can be used together with the Law of Cosines or the Law of Sines to solve problems involving physical quantities such as force, velocity, & acceleration. Ex 4) Aviation An airplane has an air speed of 520 mi/h and a heading of 115°. Wind blows from the east at 37 mi/h. Find the plane’s ground speed (norm of ground velocity) and course. course heading ground velocity wind velocity N so course is ° air velocity N 115° °

Homework #1207 Pg 643 #1, 5, 10, 13, 18, 20, 27, 29, 30, 32, 35–39 all