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Questions and Answers
What is the definition of a vector in algebra?
What is the definition of a vector in algebra?
- A quantity with only magnitude
- A quantity with only direction
- A quantity with both magnitude and direction (correct)
- A quantity with neither magnitude nor direction
What is the result of adding two vectors of the same direction?
What is the result of adding two vectors of the same direction?
- A scalar quantity
- A vector with a magnitude equal to the sum of the magnitudes of the individual vectors and the same direction (correct)
- A vector with a magnitude equal to the difference of the magnitudes of the individual vectors and the same direction
- A vector with a magnitude equal to the sum of the magnitudes of the individual vectors and the opposite direction
What is the cross product of two vectors used to calculate?
What is the cross product of two vectors used to calculate?
- The area of the parallelogram formed by the two vectors (correct)
- The magnitude of the two vectors
- The projection of one vector onto the other
- The angle between the two vectors
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Study Notes
Vectors in Algebra
- A vector is a quantity with both magnitude (length) and direction, represented graphically as an arrow in a coordinate system.
Vector Addition
- When adding two vectors of the same direction, the result is a vector with the same direction, and the magnitude is the sum of the magnitudes of the individual vectors.
Cross Product
- The cross product of two vectors is used to calculate the area of the parallelogram spanned by the two vectors, as well as the direction of the resulting vector, which is perpendicular to both original vectors.
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