Pre Lab
As you know, vectors are special kinds of numbers that include both magnitude and direction. We have done various algebraic and trigonometric manipulations of vectors in the past. This week we will explore several forms of vector multiplication that we use in a variety of different physics contexts/
There are three forms of vector multiplication: multiplication by a scalar, dot product, and cross product. Each of these is done in a different way and produces a different kind of result.
Multiplication by a scalar (not surprisingly) is when you multiply a vector by a scalar. The scalar "scales" the vector, changing its length by a factor of the magnitude of the scalar. For instance the scalar 3 multiplied by vector A will result in a vector three times larger in magnitude and in the same direction as A. The dot product (AKA the scalar product) multiplies two vectors, picking out the components of those vectors that are parallel. Dot products result in a scalar quantity. Work is a common dot product in physics, W = F • d. The dot product is defined as follows: A•B = |A| |B| cos(ѳ). Note that the dot product is maximized when the vectors are parallel. The video on the right explains the process for calculating dot products in detail.
The cross product (AKA the vector product) multiplies two vectors, picking out the components of those vectors that are perpendicular. Cross products result in a vector quantity. Torque is a common dot product in physics, torque = r x F. The cross product is defined as follows: AxB = |A| |B| sin(ѳ) n. The n following this equation should have a hat (small carrot) over it. Two Notes: 1) the cross product is maximized when the vectors are perpendicular, 2) the cross product result is a vector directed normal (perpendicular) to the other two vectors. The video on the right explains the process for calculating cross products using matrix algebra in detail. In the lab this week we will 1) calculating dot and cross products, and 2) the applications of dot and cross products in physics. Prior to lab please complete the following:
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A few videos about Multiplying Vectors
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Pre Lab Video
Simulation
Explore the simulation and calculators embedded at the following link to explore vector multiplication.
Simulation: https://www.edumedia-sciences.com/en/media/198-dot-product
Dot Product Calculator: www.symbolab.com/solver/vector-dot-product-calculator
Cross Product Calculator: www.symbolab.com/solver/vector-cross-product-calculator
You may use these to answer the pre lab quiz questions as well.
Pre-Lab Quiz is available at the course Blackboard website
Simulation: https://www.edumedia-sciences.com/en/media/198-dot-product
Dot Product Calculator: www.symbolab.com/solver/vector-dot-product-calculator
Cross Product Calculator: www.symbolab.com/solver/vector-cross-product-calculator
You may use these to answer the pre lab quiz questions as well.
Pre-Lab Quiz is available at the course Blackboard website
Lab
This week you will be completing the Multiplying Vectors Lab (pg 81) found your lab manual.
We will be using your brain to complete this lab.
We will be using your brain to complete this lab.
Post Lab
Please post a reflection on the lab experience on the Faraday's Law Lab Reflection discussion board on the course Blackboard site.
Be sure to include:
Be sure to include:
- What you did
- Why you did it
- Any interesting observations
- What you learned from doing the lab