NEB Class 11 • Mathematics • Vectors • Practice Set

Linear Combination, Dependence & Independence of Vectors Practice Set: NEB 11 Maths

Master Linear Combination, Dependence and Independence of Vectors through clear concepts, representations, a reliable answer method and exam-focused practice.

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Concepts · Worked reasoning · NEB practice

Quick answer: A linear combination builds a vector from weighted vectors. A set is dependent when a nontrivial combination equals zero; independence means only the all-zero coefficients do so.

Worked practice

Build the result from meaning, not memory

A linear combination builds a vector from weighted vectors. A set is dependent when a nontrivial combination equals zero; independence means only the all-zero coefficients do so.

Worked example

(1,2) and (2,4) are dependent because 2(1,2)−(2,4)=0, while (1,0) and (0,1) are independent.

The governing relationship is Vectors v₁,…,vₙ are dependent if c₁v₁+…+cₙvₙ=0 for coefficients not all zero; for square coordinate matrices, determinant zero signals dependence. Check the convention, geometry or boundary condition before calculation.

Independent practice ladder

  1. Define the key physical quantities and give their SI units.
  2. Draw and label the relevant wave, ray, mode or energy diagram.
  3. Recalculate the worked example after changing one input by a factor of two.
  4. Explain the result without equations.
  5. Create a Nepal-relevant situation such as a classroom speaker, musical pipe, optical slit or thermal machine.
  6. Compare two cases and predict the larger output before calculating.
  7. Find and repair one deliberately wrong sign, node or unit.
  8. Write a three-mark answer and a five-mark answer.

Answer protocol: diagram → known data → principle → symbolic equation → SI substitution → result → physical check. Calling any nonzero combination dependence, testing only pairwise non-parallelism for larger sets, or forgetting that too many vectors in a fixed dimension must be dependent.

NEB answer method

Model → evidence → equation → check

First identify the system and what the question asks. Label the diagram, apparatus or reaction with SI quantities, then state the principle before selecting an equation. Solve symbolically where possible and check units, limiting cases and chemical or physical meaning.

StageQuestionEvidence
ModelWhat is idealised?Assumption stated
RepresentationWhich diagram fits?Labels or balanced equation
CalculationWhich relation follows?Symbols then SI values
EvaluationDoes it make sense?Unit, sign and trend check

Make the idea concrete in Nepal

Connect the model to a school laboratory, household technology, health, environment, energy or local material. The example should clarify the science rather than merely mention a place. Compare a prediction with an observation and record uncertainty.

Review the NEB Class 11 Mathematics revision roadmap and the complete Mathematics guide. For online or physical tuition, call 9846662070.

Questions students ask about Linear Combination, Dependence and Independence of Vectors

What is the central idea of Linear Combination, Dependence and Independence of Vectors?

A linear combination builds a vector from weighted vectors. A set is dependent when a nontrivial combination equals zero; independence means only the all-zero coefficients do so.

Which equation should I remember?

Vectors v₁,…,vₙ are dependent if c₁v₁+…+cₙvₙ=0 for coefficients not all zero; for square coordinate matrices, determinant zero signals dependence.

How should I begin a numerical?

Draw the situation, list known quantities in SI units, choose the governing relation symbolically, substitute once and finish with a unit and reasonableness check.

What is a common exam mistake?

Calling any nonzero combination dependence, testing only pairwise non-parallelism for larger sets, or forgetting that too many vectors in a fixed dimension must be dependent.

How can I practise this topic?

Alternate one concept explanation, one diagram and two numericals. Revisit errors after a day instead of only rereading the solution.

Where can I get tuition support?

For online or physical KTM Tuition classes, call 9846662070. After Grade 12, the MKS Education panel below gives preparation and pre-counselling contacts.

Frequently asked questions

References and next steps

Scope checked against CDC Nepal; concept support from an institutional reference and OpenStax Science. Continue with the Linear Combination, Dependence and Independence of Vectors cluster.

NEB +2 tuition support

Ask about online or physical tuition

For focused Class 11 and Class 12 subject tuition, lesson clarification, worked-example practice and exam preparation, call 9846662070. Class mode, timetable, teacher availability and fees should be confirmed directly before enrolment.

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