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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?
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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 the Dot Product
The operation used to obtain a scalar from two vectors is known as the dot product. This is a fundamental concept in vector mathematics, especially in physics and engineering.
Definition of Dot Product
- The dot product of two vectors A and B is calculated as the sum of the products of their corresponding components.
- Mathematically, if A = (a1, a2, a3) and B = (b1, b2, b3), then the dot product A · B = a1*b1 + a2*b2 + a3*b3.
Characteristics of Dot Product
- Result: The result of a dot product is a scalar quantity, which means it has magnitude but no direction.
- Angle Dependency: The dot product can also be expressed in terms of the angle θ between the two vectors: A · B = |A| |B| cos(θ). This shows how the angle influences the result.
Applications of Dot Product
- Projection: The dot product helps in finding the projection of one vector onto another.
- Work Calculation: In physics, the dot product is used to calculate work done when a force is applied along a distance.
Why Other Options Are Incorrect
- Cross Product: Produces a vector, not a scalar.
- Simple Product: Typically refers to multiplication of numbers, not vectors.
- Complex Product: Involves complex numbers, not relevant to the scalar output from vectors.
In summary, the dot product is the correct operation to obtain a scalar from two vectors due to its definition, properties, and applications in various fields.
The operation used to obtain a scalar from two vectors is known as the dot product. This is a fundamental concept in vector mathematics, especially in physics and engineering.
Definition of Dot Product
- The dot product of two vectors A and B is calculated as the sum of the products of their corresponding components.
- Mathematically, if A = (a1, a2, a3) and B = (b1, b2, b3), then the dot product A · B = a1*b1 + a2*b2 + a3*b3.
Characteristics of Dot Product
- Result: The result of a dot product is a scalar quantity, which means it has magnitude but no direction.
- Angle Dependency: The dot product can also be expressed in terms of the angle θ between the two vectors: A · B = |A| |B| cos(θ). This shows how the angle influences the result.
Applications of Dot Product
- Projection: The dot product helps in finding the projection of one vector onto another.
- Work Calculation: In physics, the dot product is used to calculate work done when a force is applied along a distance.
Why Other Options Are Incorrect
- Cross Product: Produces a vector, not a scalar.
- Simple Product: Typically refers to multiplication of numbers, not vectors.
- Complex Product: Involves complex numbers, not relevant to the scalar output from vectors.
In summary, the dot product is the correct operation to obtain a scalar from two vectors due to its definition, properties, and applications in various fields.
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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 NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET 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 NEET 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 NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET 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 NEET 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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