Dot Product
Easymathematics
The dot product of vectors a and b is defined as
Select the correct option:
Solution
Incorrect! Answer:
|a||b|cos θ
- Scalar Product Definition: The dot product results in a scalar value.
- Geometric Formula: a⋅b=∣a∣∣b∣cosθ, where θ is the angle between the two vectors.
- Physical Meaning: It represents the projection of one vector onto the other multiplied by the other's magnitude.
- Range: Value is positive for acute angles, zero for orthogonal vectors, and negative for obtuse angles.
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About This Question
- Subject
- mathematics
- Chapter
- vector algebra
- Topic
- dot product
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
|a||b|cos θ
- Scalar Product Definition: The dot product results in a scalar value.
- Geometric Formula: a⋅b=∣a∣∣b∣cosθ, where θ is the angle between the two vectors.
- Physical Meaning: It represents the projection of one vector onto the other multiplied by the other's magnitude.
- Range: Value is positive for acute angles, zero for orthogonal vectors, and negative for obtuse angles.
This easy difficulty mathematics question is from the chapter vector algebra, covering the topic of dot product. It appeared in the 2025 exam.
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