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Vector Algebra
Mathematics
Useful for: UPSC NDA/NA
Overview
Vectors have magnitude and direction; dot and cross products measure angles, projections, areas and perpendicularity.
Key points
- Magnitude of (a, b, c) = √(a² + b² + c²).
- Dot product a · b = |a||b| cos θ; perpendicular vectors have dot product zero.
- Cross product magnitude |a × b| = |a||b| sin θ; it is perpendicular to both vectors.
- i · j = 0 and i × j = k.
- Unit vector = vector ÷ its magnitude.
- Area of a parallelogram = |a × b|.
Practice MCQs
From the perspective of definition and scope, which one of the following statements about Vector Algebra is correct?
- Vector Algebra is unrelated to institutions, processes or real-world applications.
- Vector Algebra has no exceptions or limitations in exam analysis.
- Vector Algebra questions reward a formula-first approach and accurate algebraic manipulation.
- Do not apply a memorized Vector Algebra formula without checking its conditions.
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Answer: (c) Vector Algebra questions reward a formula-first approach and accurate algebraic manipulation.. Vector Algebra questions reward a formula-first approach and accurate algebraic manipulation.
Consider the following statements on Vector Algebra and Probability, focusing on definition and scope: 1. Do not apply a memorized Vector Algebra formula without checking its conditions. 2. Do not apply a memorized Probability formula without checking its conditions. Which of the statements given above is/are correct?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
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Answer: (d) Neither 1 nor 2. Neither statement is correct; both are common misconceptions.
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