Dot Product Completed 2016.notebook

December 07, 2016

A ball is thrown at 25mph at an angle of 30○. What is the initial speed in the horizontal direction of the ball? What is the initial speed in the vertical direction of the ball?

Dot Product Completed 2016.notebook

December 07, 2016

A bullet is fired from a gun at 220mph at an angle of 40○. What is the initial speed in the horizontal direction of the bullet What is the initial speed in the vertical direction of the bullet?

Dot Product Completed 2016.notebook

December 07, 2016

A bullet is fired from a gun at 220mph at an angle of 40○. What is the initial speed in the horizontal direction of the bullet What is the initial speed in the vertical direction of the bullet?

Dot Product Completed 2016.notebook

December 07, 2016

An airplane is traveling at a constant speed of 375mph at a  heading of N30○W. Express the velocity of the plane as a vector.

Dot Product Completed 2016.notebook

December 07, 2016

An airplane is traveling at a constant speed of 375mph at a  heading of N30○W. Express the velocity of the plane as a vector.

Dot Product Completed 2016.notebook

December 07, 2016

An airplane is traveling at a constant speed of 420 mph at a  heading of S40○E. Express the velocity of the plane as a vector.

Dot Product Completed 2016.notebook

December 07, 2016

An airplane is traveling at a constant speed of 420 mph at a  heading of S40○E. Express the velocity of the plane as a vector.

Dot Product Completed 2016.notebook

December 07, 2016

Dot Product Completed 2016.notebook

December 07, 2016

Review Multiplying Vectors Scalar Multiplication – What are you multiplying together?

What kind of answer do you get?

Dot Product Completed 2016.notebook

December 07, 2016

Dot Product Terminology:  Dot Product = Scalar Product = Inner Product Multiplying 2 vectors together

What kind of answer will this give you?

Dot Product Completed 2016.notebook

Examples:

December 07, 2016

Dot Product Completed 2016.notebook

What happens if you dot a vector with itself?

What does this really give you?

December 07, 2016

Dot Product Completed 2016.notebook

Properties of dot product

December 07, 2016

Dot Product Completed 2016.notebook

December 07, 2016

Angle between two vectors How could we find the angle between 2 vectors?

Dot Product Completed 2016.notebook

A Different way to define the Dot Product:  

December 07, 2016

Dot Product Completed 2016.notebook

Find the angle between vectors v and w.

December 07, 2016

Dot Product Completed 2016.notebook

Orthogonal and Parallel Vectors

What does it mean for 2 vectors to be parallel?

Let’s draw some parallel vectors.

What would be the angle between these vectors?

December 07, 2016

Dot Product Completed 2016.notebook

December 07, 2016

Orthogonal and Parallel Vectors What does it mean for 2 vectors to be orthogonal? (normal, perpendicular)

Let’s draw some orthogonal vectors.

What would be the angle between these vectors?

When will this happen?

Dot Product Completed 2016.notebook

December 07, 2016

Work Work is a measurement of the force required to MOVE an object.

A force (in lbs) is given by F = 4i + 8j and moves an object (in ft)  from (2, 5) to (9, 12).  Find the amount of work that is done.

Dot Product Completed 2016.pdf

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