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The operation used to obtain a scalar from two vectors is ______
- a)Cross product
- b)Dot product
- c)Simple product
- d)Complex product
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The operation used to obtain a scalar from two vectors is ______a)Cros...
Dot product of two vectors gives a scalar quantity as the output. Cross product gives a vector as the output. It is also known as scalar product.
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The operation used to obtain a scalar from two vectors is ______a)Cros...
Understanding Scalar Operations from Vectors
When dealing with vectors, there are specific operations that can yield different types of results. One such operation that produces a scalar is the Dot Product.
What is the Dot Product?
- The dot product, also known as the scalar product, is an operation that takes two vectors and returns a single scalar value.
- Mathematically, if you have two vectors A and B, the dot product is calculated as:
- A · B = |A| |B| cos(θ)
- Here, |A| and |B| are the magnitudes of the vectors, and θ is the angle between them.
Properties of the Dot Product
- Commutative: A · B = B · A
- Distributive: A · (B + C) = A · B + A · C
- Associative with Scalars: k(A · B) = (kA) · B = A · (kB)
Applications of the Dot Product
- The dot product is crucial in various applications, including:
- Determining the angle between two vectors.
- Assessing the projection of one vector onto another.
- Calculating work done when a force is applied along a displacement.
Conclusion
In summary, the operation used to obtain a scalar from two vectors is the Dot Product. It serves as a fundamental tool in vector mathematics, enabling calculations that are pivotal in physics and engineering. Understanding this operation is essential for solving various problems involving vectors.
When dealing with vectors, there are specific operations that can yield different types of results. One such operation that produces a scalar is the Dot Product.
What is the Dot Product?
- The dot product, also known as the scalar product, is an operation that takes two vectors and returns a single scalar value.
- Mathematically, if you have two vectors A and B, the dot product is calculated as:
- A · B = |A| |B| cos(θ)
- Here, |A| and |B| are the magnitudes of the vectors, and θ is the angle between them.
Properties of the Dot Product
- Commutative: A · B = B · A
- Distributive: A · (B + C) = A · B + A · C
- Associative with Scalars: k(A · B) = (kA) · B = A · (kB)
Applications of the Dot Product
- The dot product is crucial in various applications, including:
- Determining the angle between two vectors.
- Assessing the projection of one vector onto another.
- Calculating work done when a force is applied along a displacement.
Conclusion
In summary, the operation used to obtain a scalar from two vectors is the Dot Product. It serves as a fundamental tool in vector mathematics, enabling calculations that are pivotal in physics and engineering. Understanding this operation is essential for solving various problems involving vectors.
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The operation used to obtain a scalar from two vectors is ______a)Cross productb)Dot productc)Simple productd)Complex productCorrect answer is option 'B'. Can you explain this answer?
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The operation used to obtain a scalar from two vectors is ______a)Cross productb)Dot productc)Simple productd)Complex productCorrect answer is option 'B'. Can you explain this answer? for Grade 10 2025 is part of Grade 10 preparation. The Question and answers have been prepared according to the Grade 10 exam syllabus. Information about The operation used to obtain a scalar from two vectors is ______a)Cross productb)Dot productc)Simple productd)Complex productCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Grade 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The operation used to obtain a scalar from two vectors is ______a)Cross productb)Dot productc)Simple productd)Complex productCorrect answer is option 'B'. Can you explain this answer?.
The operation used to obtain a scalar from two vectors is ______a)Cross productb)Dot productc)Simple productd)Complex productCorrect answer is option 'B'. Can you explain this answer? for Grade 10 2025 is part of Grade 10 preparation. The Question and answers have been prepared according to the Grade 10 exam syllabus. Information about The operation used to obtain a scalar from two vectors is ______a)Cross productb)Dot productc)Simple productd)Complex productCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Grade 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The operation used to obtain a scalar from two vectors is ______a)Cross productb)Dot productc)Simple productd)Complex productCorrect answer is option 'B'. Can you explain this answer?.
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