Math Problem Statement
Compute each of the cross products: ixj=? ixk=? jxk=?
Solution
The cross product of two standard unit vectors in 3D space () can be determined using the properties of the cross product. Here are the results:
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: This is because the cross product of two perpendicular unit vectors results in the third unit vector that completes the right-handed coordinate system.
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: This is the result of the cross product between and . It gives a vector that is perpendicular to both, but with the negative sign since the order matters (cross product is anti-commutative).
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: This follows the same reasoning, resulting in a vector perpendicular to both and , in the positive direction according to the right-hand rule.
To summarize:
Would you like more details or have any questions?
Related Questions:
- What is the result of ?
- How does the right-hand rule help determine the direction of cross products?
- What are the properties of the cross product in vector algebra?
- Can cross products be computed in dimensions other than three?
- How do you compute the cross product of two arbitrary vectors?
Tip: The cross product of vectors is useful for finding a vector perpendicular to a plane formed by two vectors.
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Math Problem Analysis
Mathematical Concepts
Vector Algebra
Cross Product
3D Coordinate System
Formulas
i × j = k
i × k = -j
j × k = i
Theorems
Right-hand Rule
Anticommutativity of Cross Product
Suitable Grade Level
Grades 10-12