CROSS[1]

# CROSS[1] - THE CROSS PRODUCT We met this before when we...

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THE CROSS PRODUCT We met this before when we studied torques! The geometrical definition of a cross product is AB x CB C s i n   where θ is the angle FROM as shown in the drawing: BtoC OK, so far, so good. This gives us the magnitude, but not the direction. For this, we need to use our “circle”. B C θ ˆ x ˆ y ˆ z

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Let’s do a simple problem:  ˆˆ A3 x2 z B 4 y2 z What is A B? A B 3x 2z 4y 2z In elementary algebra, we learned the F.O.I.L. rule for multiplying two binomials together: F.O.I.L stands for First, Outside, Inside, Last. The           cross product becomes: AB 3 4xy 3 2xz 2 4zy 2 2zz AB 1 2xy 6xz 8zy 4zz To do the cross products of the unit vectors in the square brackets, we look to the circle! Put yo              
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CROSS[1] - THE CROSS PRODUCT We met this before when we...

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The text passage provides an explanation of the cross product in vector mathematics, including its geometrical definition and a step-by-step example of how to compute a cross product using unit vectors. It also mentions the F.O.I.L. rule for multiplying binomials and how it applies to the cross product of vectors.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
CROSS[1]

# CROSS[1] - THE CROSS PRODUCT We met this before when we...

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THE CROSS PRODUCT We met this before when we studied torques! The geometrical definition of a cross product is AB x CB C s i n   where θ is the angle FROM as shown in the drawing: BtoC OK, so far, so good. This gives us the magnitude, but not the direction. For this, we need to use our “circle”. B C θ ˆ x ˆ y ˆ z

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Let’s do a simple problem:  ˆˆ A3 x2 z B 4 y2 z What is A B? A B 3x 2z 4y 2z In elementary algebra, we learned the F.O.I.L. rule for multiplying two binomials together: F.O.I.L stands for First, Outside, Inside, Last. The           cross product becomes: AB 3 4xy 3 2xz 2 4zy 2 2zz AB 1 2xy 6xz 8zy 4zz To do the cross products of the unit vectors in the square brackets, we look to the circle! Put yo              
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CROSS[1] - THE CROSS PRODUCT We met this before when we...

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The text passage provides an explanation of the cross product in vector mathematics, including its geometrical definition and a step-by-step example of how to compute a cross product using unit vectors. It also mentions the F.O.I.L. rule for multiplying binomials and how it applies to the cross product of vectors.

TYPE: SINGLE_QUESTION_WITH_ANSWER