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NCERT Solutions · Class 12 · Chapter 10: Vector Algebra

NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1

Exercise 10.1: Vectors and their types. A scalar has magnitude only; a vector has magnitude and direction. Equal vectors: same magnitude and same direction (wherever they start). Collinear vectors lie along parallel lines, in the same or opposite direction. Coinitial vectors start at the same point.

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Exercise 10.1 questions and solutions

Exercise 10.1, Question 1

Represent a displacement of 40 km, \(30^\circ\) east of north.
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  1. Draw a north direction, turn \(30^\circ\) towards east, and draw an arrow of length 4 units on a scale of 1 unit = 10 km.
Answer: An arrow of 4 units (scale 1 : 10 km) at \(30^\circ\) east of north

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Exercise 10.1, Question 2

Classify as scalar or vector.
(i) 10 kg (ii) 2 metres north-west (iii) \(40^\circ\) (iv) 40 watt (v) \(10^{-19}\) coulomb (vi) 20 m/s\(^2\)
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  1. Only (ii) (a displacement) and (vi) (an acceleration, which has a direction) carry direction.
Answer: Scalars: (i), (iii), (iv), (v). Vectors: (ii), (vi)

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Exercise 10.1, Question 3

Classify as scalar or vector quantities.
(i) time period (ii) distance (iii) force (iv) velocity (v) work done
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  1. Force and velocity have direction; time, distance and work do not.
Answer: Scalars: time period, distance, work done. Vectors: force, velocity

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Exercise 10.1, Question 4

In the square of Fig 10.6, \(\vec a\) runs along the top edge (left to right), \(\vec b\) down the right edge, \(\vec c\) along the bottom edge (right to left) and \(\vec d\) down the left edge.
Identify (i) coinitial vectors (ii) equal vectors (iii) collinear but not equal vectors.
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  1. \(\vec a\) and \(\vec d\) both start at the top-left corner.
  2. \(\vec b\) and \(\vec d\) are parallel sides of equal length, both pointing down.
  3. \(\vec a\) and \(\vec c\) are parallel but point in opposite directions.
Answer: (i) \(\vec a, \vec d\) (ii) \(\vec b, \vec d\) (iii) \(\vec a, \vec c\)

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Exercise 10.1, Question 5

True or false?
(i) \(\vec a\) and \(-\vec a\) are collinear.
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  1. They lie along the same line, in opposite directions.
Answer: True
(ii) Two collinear vectors are always equal in magnitude.
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  1. \(\vec a\) and \(2\vec a\) are collinear with different magnitudes.
Answer: False
(iii) Two vectors with the same magnitude are collinear.
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  1. \(\hat i\) and \(\hat j\) both have magnitude 1 but are perpendicular.
Answer: False
(iv) Two collinear vectors with the same magnitude are equal.
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  1. \(\vec a\) and \(-\vec a\): same magnitude, collinear, not equal.
Answer: False

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Done the NCERT exercises? The board paper asks more

Vector Algebra has 39 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.

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Vector Algebra in our sample papers: Sample paper 1 (questions 13, 15, 24) · Sample paper 2 (questions 16, 19, 34) · Sample paper 3 (questions 13, 14, 24) · Sample paper 4 (questions 16, 19, 25) · Sample paper 5 (questions 13, 19, 24).

Also useful: free MCQs and case studies for Vector Algebra · formulas for this chapter (Class 12 formula sheet, free PDF) · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan

Textbook: NCERT Mathematics Class 12, Parts I and II (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.