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Assertion (A) : The vectors… (Class 12 Maths 2024, Q20)

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MathsCBSE Class 12 · Board exam 2024, set 65/5/1 · 1 mark · Assertion-reason

CBSE Class 12 Mathematics 2024: question 20

Set in the CBSE Class 12 board exam of 2024, paper 65/5/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedVector Algebra

Assertion (A) : The vectors , , represent the sides of a right angled triangle.

Reason (R) : Three non-zero vectors of which none of two are collinear forms a triangle if their resultant is zero vector or sum of any two vectors is equal to the third.

  1. (A)Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
  2. (B)Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of the Assertion (A).
  3. (C)Assertion (A) is true, but Reason (R) is false.
  4. (D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 65/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Check whether one vector equals the sum of the other two.

Hint 2

Look for a pair of vectors whose dot product is zero.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. , so the three vectors form a triangle. Also , so there is a right angle; the Assertion is true.

    ½ mark

  2. The Reason is a true statement, but the right angle comes from the dot product being zero, not from the Reason. The answer is option (B).

    ½ mark

Answer: (B)

Where the marks are

  • Verifies the triangle and the right angle, and judges the explanation (1 mark)

Revise the chapter

  • Chapter: Vector Algebra (notes, formulas, where marks are lost and every past question)
Practise this chapterBoard-style questions from Vector Algebra, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 65/5/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.