NCERT Solutions For Class 12 Maths Exercise 10.1: Vector Algebra - Future Study Point

NCERT Solutions For Class 12 Maths Exercise 10.1: Vector Algebra

NCERT Solutions For Class 12 Maths Exercise 10.1: Vector Algebra

NCERT Solutions For Class 12 Maths Exercise 10.1: Vector Algebra

NCERT Solutions For Class 12 Maths Exercise 10.1: Vector Algebra

NCERT Solutions For Class 12 Maths Exercise 10.1: Vector Algebra is introduced here for clearing the concept about the way of solutions of unsolved questions of Class 12 Maths exercise 10.1: Vector Algebra, the NCERT Class 12  Maths exercise 10.1 is an introduction exercise of chapter 10 : Vector Algebra, therefore it is important for class 12 students to understand the concept of Vector Algebra before studying another complicated exercises of chapter 10: Vector Algebra.

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NCERT solutions for class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
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NCERT Solutions For Class 12 Maths Exercise 10.1: Vector Algebra

Q1.Represent graphically a displacement of 40 km, 30° east of north.

Solution:

Q1 ex.10.1 class 12 maths

   represents the displacement of  40 km,40° east of the north.

Q2. Classify the following measures as scalars and vectors.

(i) 10 kg (ii) 2 metres north-west (iii) 40°

(iv) 40 watt (v) 10–19 coulomb (vi) 20 m/s2

Solution: (i)10 Kg represents magnitude only, therefore it is a scaler.

(ii) 2 metres north-west, shows direction as well as magnitude, therefore it is a vector.

(iii) 40°, represents magnitude only, therefore it is a scaler.

(iv) 40 watts, represents magnitude only, therefore it is a scaler.

(v) 10–19 coulomb, represents magnitude only, therefore it is a scaler.

(vi) 20 m/s2   shows that the velocity of the object is increasing at the rate of 20 m/s2 , therefore it represents direction as well as magnitude, therefore it is a vector.

Q3. Classify the following as scalar and vector quantities.

(i) Time period (ii) Distance (iii) Force

(iv) Velocity (v) Work done

Ans.(i) Time period, for example, 2 months,3 hours etc shows magnitude only,therefore it is a scaler.

(ii) Distance, for example, 2 km,3 m etc shows magnitude only, therefore it is a scaler.

(iii) Force, F = ma, m(mass) is a scaler and a , acceleration is a vector, therefore it represents direction as well as magnitude, therefore it is a vector.

(iv) Velocity, represents direction as well as magnitude, therefore it is a vector.

(v) Work done shows magnitude only, therefore it is a scaler.

Q4. In Figure, identify the following vectors.

Q4 ex.10.1 class 12 maths

(i) Coinitial (ii) Equal (iii) Collinear but not equal

Ans.(i)   and are initiated from the same point, therefore both of them are coinitial.

(ii) and have equal magnitude and same direction, therefore both of them are equal.

(iii) and are collinear but not equal because their directions are different.

Q5. Answer the following as true or false.

(i)  and   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.

Solution: (i) True ,  and  are collinear vectors because both of them parallel to the same line .

(ii) False, for being collinear, vectors should be parallel to the same line.

(iii)  False, two vectors having the same magnitude are not necessarily collinear because two vectors are collinear only when they are parallel to each other.

(iv) False,two vectors having the same magnitude and direction are called equal vectors.

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