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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...
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.
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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)Cross productb)Dot productc)Simple productd)Complex productCorrect answer is option 'B'. Can you explain this answer?
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