Ncert Solutions For Class 12 Maths Ex 10.1

Ncert Solutions For Class 12 Maths Chapter 10 Ex 10.1

Question 1: Graphically represent a 40 km displacement towards 30 o east of north.

Answer 1:

Vector \(\overrightarrow{OP}\) represent a 40 km displacement towards 30o east of north.

 

Question 2: Categorize the following measures as vectors and scalars.

(a) 20 kg (b) 4 meters north – south (c) 80o

(d) 70 watt (e) 10– 17 coulomb (f) 56 m / s– 2

Answer 2:

(a) In 20 kg, only magnitude is involved. So, it is a scalar quantity.

(b) In 4 meters north – south, both the direction and magnitude are involved. So, it is a vector quantity

(c) In 80o, only magnitude is involved. So, it is a scalar quantity.

(d) In 70 watt, only magnitude is involved. So, it is a scalar quantity.

(e) In 10 – 17 coulombs, only magnitude is involved. So, it is a scalar quantity.

(f) In 56 m / s– 2, both the direction and magnitude are involved. So, it is a vector quantity

 

 

Question 3: Categorize the following quantities as vector and scalar.

(a) Time period (b) distance (c) force

(d) Velocity (e) work done

Answer 3:

(a) In time period, only magnitude is involved. So, it is a scalar quantity.

(b) In distance, only magnitude is involved. So, it is a scalar quantity.

(c) In force, both the direction and magnitude are involved. So, it is a vector quantity

(d) In velocity, both the direction and magnitude are involved. So, it is a vector quantity

(e) In work done, only magnitude is involved. So, it is a scalar quantity.

Question 4: In the following diagram, recognize the corresponding vectors

(a) Coinitial

(b) Equal

(c) Collinear but not equal

Answer 4:

(a) Coinitial vectors are those vectors which have same initial point. So, \(\overrightarrow{a} \;and\; \overrightarrow{d}\) vectors are coinitial.

(b) Equal vectors are vectors which have same magnitude and direction. So, \(\overrightarrow{b} \;and\; \overrightarrow{d}\) vectors are equal.

(c) Collinear but not equal are those vectors which are parallel but has different directions. So, \(\overrightarrow{a} \;and\; \overrightarrow{c}\) vectors are collinear but not equal.

Question 5: Check whether the following statements are true or false.

(a) \(\overrightarrow{b} \;and\; \overrightarrow{- b}\) vectors are collinear

(b) The magnitudes of the two collinear are always equal.

(c) Collinear vectors are the two vectors having same magnitude.

Answer 5:

(a). True because the two vectors are parallel .

(b). False because collinear vectors must be parallel.

(c). False.