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JEE Advanced Unit 9A: Parametric Equations and Plane Curves — practice questions

Explore 43 free Unit 9A: Parametric Equations and Plane Curves questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 9A: Parametric Equations and Plane Curves questions and exercises with answers

Showing questions 1–30 of 43.

A quantity having only magnitude (no direction) is called:Read the answer and worked solution →Vector addition is:Read the answer and worked solution →The dot product ā · b̄ is:Read the answer and worked solution →The cross product ā × b̄ is:Read the answer and worked solution →What is î × ĵ?Read the answer and worked solution →Two vectors are PERPENDICULAR iff:Read the answer and worked solution →Two vectors are PARALLEL (or anti-parallel) iff:Read the answer and worked solution →The MAGNITUDE of a × b equals:Read the answer and worked solution →Find magnitude of ā = 3î + 4ĵ:Read the answer and worked solution →Find ā · b̄ if ā = 2î + 3ĵ and b̄ = î - 2ĵ:Read the answer and worked solution →Find ā × b̄ where ā = î + 2ĵ + k̂ and b̄ = 2î + ĵ + 3k̂:Read the answer and worked solution →Angle between two vectors ā = 2î + 2ĵ and b̄ = 4î - 4ĵ:Read the answer and worked solution →Find unit vector in direction of ā = 3î + 4ĵ:Read the answer and worked solution →Area of parallelogram formed by ā and b̄ equals:Read the answer and worked solution →Position vectors of P and Q are p̄ and q̄. The point R divides PQ internally in ratio m:n. Position vector of R:Read the answer and worked solution →Three vectors ā, b̄, c̄ are coplanar iff their SCALAR TRIPLE PRODUCT [ā b̄ c̄] equals:Read the answer and worked solution →For vectors ā = î + ĵ and b̄ = î - ĵ, find |ā + b̄|:Read the answer and worked solution →Projection of ā = 3î + 4ĵ on b̄ = î + ĵ:Read the answer and worked solution →If ā × b̄ = 0 and neither is the zero vector, then:Read the answer and worked solution →Volume of parallelepiped formed by ā, b̄, c̄:Read the answer and worked solution →For unit vectors î, ĵ, k̂: î · ĵ + ĵ · k̂ + k̂ · î =Read the answer and worked solution →For vectors ā = î - ĵ + 2k̂ and b̄ = 3î + 2ĵ - k̂, find the AREA of the parallelogram formed (use |ā × b̄|):Read the answer and worked solution →Find cos θ for ā = 2î + 3ĵ - 4k̂ and b̄ = î + 2ĵ + 3k̂ (where θ is the angle between them):Read the answer and worked solution →Find scalar triple product [î ĵ k̂]:Read the answer and worked solution →Vectors ā = î + 2ĵ + 3k̂ and b̄ = 2î + 3ĵ + αk̂ are perpendicular. Find α:Read the answer and worked solution →For vectors ā = î - ĵ + 2k̂ and b̄ = 3î + 2ĵ - k̂, find the area of triangle formed:Read the answer and worked solution →Find angle θ between ā = 2î + 3ĵ - 4k̂ and b̄ = î + 2ĵ + 3k̂ (use cos θ = ā·b̄/(|ā||b̄|)):Read the answer and worked solution →For ā = 2î + 3ĵ and b̄ = αî + 6ĵ to be parallel, α equals:Read the answer and worked solution →If [ā b̄ c̄] = 5, find [2ā b̄ c̄]:Read the answer and worked solution →Vector r̄ is collinear with ā = î - 2ĵ + 2k̂ and |r̄| = 12. Find r̄:Read the answer and worked solution →

Worked practice questions

A quantity having only magnitude (no direction) is called:

  1. Vector
  2. Tensor
  3. Matrix
  4. Scalar
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Correct answer: D. Scalar

Scalars have only magnitude (mass, temperature, time). Vectors have both magnitude AND direction (velocity, force, displacement).

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Vector addition is:

  1. Non-commutative
  2. Commutative (a+b = b+a)
  3. Always zero
  4. Sometimes commutative
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Correct answer: B. Commutative (a+b = b+a)

**Vector addition is commutative:** ā + b̄ = b̄ + ā. (Also associative: (ā+b̄)+c̄ = ā+(b̄+c̄). But cross product is non-commutative.)

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The dot product ā · b̄ is:

  1. A vector
  2. A scalar
  3. Zero always
  4. Always positive
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Correct answer: B. A scalar

Dot product yields a SCALAR (number). It's |ā||b̄|cos θ where θ is the angle between vectors. Cross product yields a vector.

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More Mathematics topics

Vector Algebra and 3D GeometryStatistics and ProbabilityContinuity, Differentiability & DerivativesIntegrals and ApplicationsMatrices and DeterminantsRelations, Functions & Inverse TrigonometryStraight Lines and Conic SectionsDeterminants