## NCERT Solutions for Class 12 Maths Exercise 10.1 Chapter 10 Vector Algebra â€“ FREE PDF Download

Free PDF download of NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1 (Ex 10.1) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 12 Maths Chapter 10 Vector Algebra Exercise 10.1 Questions with Solutions to help you to revise complete Syllabus and Score More marks.

# NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra (Ex 10.1) Exercise 10.1

**1. Represent graphically a displacement of 40 km,Â**

**Â East of North.**

**Ans.Â**Displacement 40 km,Â Â East of North

Â Displacement vectorÂ Â (say) such thatÂ Â = 40 km (given) and vectorÂ Â makes an angleÂ Â with North in East-North quadrant.

**2. Check the following measures as scalars and vectors:**

**(i) 10 kg (ii) 2 meters north-west (iii)Â
**

(iv) 40 Watt

(v)Â

(iv) 40 Watt

(v)Â

**Â coulombs**

(vi) 20 m/sec

(vi) 20 m/sec

^{2}**Ans.Â (i)**Â 10 kg is a measure of mass, it has no direction, it is magnitude only and therefore it is a scalar.

**(ii)**Â 2 meters North-West is a measure of displacement. It has magnitude and direction both and hence it is a vector.

**(iii)**Â Â is a measure of angle or temperature. It has no direction, it has magnitude only. Therefore it is a scalar.

**(iv)**Â 40 Watt is a measure of powerÂ or Rate of electricity. It has no direction, only magnitude and therefore, it is a scalar.

**(v)Â**Â coulombs is a measure of electric charge and it has magnitude only, therefore, it is a scalar.

**(vi)**Â 20 m/sec

^{2}Â is a measure of acceleration. It is a measure of rate of change of velocity, therefore, it is a vector.

**3. Classify the following as scalar and vector quantities:**

**(i) time period (ii) distance (iii) force (iv) velocity (v) work done**

**Ans.Â (i)**Â Time-scalar

**(ii)**Â Distance-scalar

**(iii)**Â Force-vector

**(iv)**Â Velocity-vector

**(v)**Â Work done-scalar

**4. In the adjoining figure, (a square) identify the following vectors:**

**
**

**(i) Co-initial (ii) Equal (iii) Collinear but not equal**

**Ans.Â**

**(i)**Â Â andÂ Â have same initial point and therefore co-initial vectors.

**(ii)**Â Â andÂ Â have same direction and same magnitude. ThereforeÂ Â andÂ Â are equal vectors.

**(iii)**Â Â andÂ Â have parallel support, so that they are collinear. Since they have opposite directions, they are not equal. HenceÂ Â andÂ Â are collinear but not equal.

**5. Answer the following as true or false:**

**(i)Â ****
****Â andÂ ****
****Â are collinear. (ii) Two collinear vectors are always equal in magnitude. (iii) Two vectors having same magnitude are collinear. (iv) Two collinear vectors having the same magnitude are equal.**

**Ans.Â (i)**Â True.

**(ii)**Â False. [ Â andÂ Â are collinear vectors butÂ Â ]

**(iii)**Â False. [ Â butÂ Â andÂ Â are vectors alongÂ axis (OX) andÂ axis (OY) respectively]

**(iv)**Â False. [ Â VectorsÂ Â andÂ Â are collinear vectors andÂ Â but we know thatÂ Â because their directions are opposite.]