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class 12 Math Chapter 7: Vectors MCQs With Explanations

Practice class 12 Math Chapter 7: Vectors MCQs with explanations for Pakistani board exams. Includes solved objective questions, answer checking, chapter revision guidance and next chapter suggestions.

MCQs / class 12 / Math / Chapter 7: Vectors
9 MCQs

Chapter 7: Vectors Objective Preparation

Use this page for direct chapter practice, answer checking and explanation review. It is available through the clean URL shown in the browser, so students can bookmark and share this exact chapter.

9Total MCQs
9With explanations
1Topics represented

Topics found: Vectors

Vectors MCQs With Explanations

Q1. Work done is given by:
Work is the dot product of force and displacement, commonly denoted as F • d; 'r' is ambiguous without context, while 'd' is standard for displacement.
Q2. If two rows or columns in scalar triple product are same then product:
The scalar triple product equals the determinant of a matrix with repeated rows/columns, which is always zero due to linear dependence.
Q3. The unit vector in the direction of V is:
A unit vector is obtained by dividing the vector by its magnitude, which is V divided by |V|.
Q4. i × j =
By the right-hand rule and standard unit vector cross product identities, i × j = k.
Q5. If U and V are parallel vectors then U × V =
The cross product of two parallel vectors is the zero vector because the sine of the angle between them is zero.
Q6. If U . V = 0, then U and V are vectors:
The dot product of two vectors is zero if and only if they are perpendicular (orthogonal), since cos(90°) = 0.
Q7. cos²α + cos²β + cos²γ =
For a vector in 3D space, the sum of the squares of the direction cosines equals 1 by definition, as they represent the cosines of angles with the coordinate axes.
Q8. The initial point of a position vector is:
A position vector originates from the origin (0,0) and terminates at a point in space, defining its location relative to the origin.
Q9. A unit vector has magnitude:
A unit vector is defined as a vector with magnitude exactly equal to 1, used to indicate direction.

After Chapter 7: Vectors, Practice Next Chapters

Once you finish these MCQs, continue with the next available chapters from Math so your revision stays chapter-wise and complete.

Chapter 7: Vectors Revision Guide

Complete the MCQs first, then review every incorrect answer against the textbook heading where that concept appears. For biology and other science subjects, pay attention to terminology, diagrams, sequence of processes, examples and differences between similar structures or functions.

This chapter page keeps the exact class, subject, chapter, question count, answer checking, explanations and follow-up chapters together, so students can revise from one focused URL instead of searching through the full book again.

class 12 Mathematics MCQ Preparation: Vectors

This page supports Intermediate Part 2 practice in Mathematics. At this stage, the main purpose is consolidating advanced concepts while balancing board revision, college assessments and admission preparation. The questions available here should be used with the current textbook and the instructions issued by the learner's school or examination board.

What Mathematics MCQs can test

In Mathematics, objective questions commonly draw on definitions, formulas, identities, properties, signs, graphs, theorem statements and short calculations. A useful answer is based on the exact wording and concept, not simply on recognising a familiar option. For this subject, learners should identify the rule being tested, perform the essential working separately and check signs, restrictions and units before selecting an option.

Vectors: focused MCQ revision

This chapter should be reviewed through its main definitions, examples, diagrams, comparisons and links with earlier Mathematics concepts.

Write a one-sentence reason for each corrected answer and note the textbook heading where the concept is explained.

Common mistakes for class 12 learners

In this subject, frequent errors include sign mistakes, using a formula outside its conditions, confusing similar properties or selecting an answer from mental arithmetic without verification. Pay special attention to links between earlier intermediate concepts and the more advanced applications introduced in the final year. When the page marks an answer as incorrect, the next step should be to identify the mistaken idea and verify it, rather than memorising the displayed answer letter.

A practical revision routine

Use mixed recall and application questions, then revisit the chapters where formulas, processes or closely related terms are confused. Before attempting the MCQs, review formulas, identities, definitions, graph behavior, theorem conditions and representative solved examples. Complete a manageable set without notes, check the result, and divide errors into missing knowledge, misunderstood concepts and careless reading. Revise the appropriate section before repeating the chapter.

How to review Vectors after the quiz

List the questions you missed from Vectors and write the textbook heading connected with each one. Explain the correct idea in your own words, then return later and answer a fresh set. This gives the chapter page a clear purpose: finding specific weaknesses in Mathematics rather than only collecting a score.

Accuracy and responsible use

Explanations are provided where they exist in the question bank, but educational databases can contain incomplete or mistaken material. Confirm disputed answers with an authoritative textbook or teacher. Ahmad Learning Hub provides a practice resource and does not claim that a question will appear in an examination or that every available item represents an official board question.