NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1 - Vector Algebra

Question 2 (1): Classify the following measures as scalars and vectors.

10Kg

Answer:

10kg is a scalar quantity as it has only magnitude.

Question 2 (2): Classify the following measures as scalars and vectors. 2 meters north west

Answer:

This is a vector quantity as it has both magnitude and direction.

Question 2 (3): Classify the following measures as scalars and vectors. $40 ^\circ$

Answer:

This is a scalar quantity as it has only magnitude.

Question 2 (4): Classify the following measures as scalars and vectors. 40 watt

Answer:

This is a scalar quantity as it has only magnitude.

Question 2 (5): Classify the following measures as scalars and vectors. $10 ^{-19} \: \: coulomb$

Answer:

This is a scalar quantity as it has only magnitude.

Question 2 (6): Classify the following measures as scalars and vectors. $20 m/s^2$

Answer:

This is a Vector quantity as it has magnitude as well as direction.by looking at the unit, we conclude that measure is acceleration which is a vector.

Question 3: Classify the following as scalar and vector quantities.
(1) time period

Answer:

This is a scalar quantity as it has only magnitude.

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

(2) distance

Answer:

Distance is a scalar quantity as it has only magnitude.

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

(3) force

Answer:

Force is a vector quantity as it has both magnitudes as well as direction.

Question 3: Classify the following as scalar and vector quantities.
(4) velocity

Answer:

Velocity is a vector quantity as it has both magnitude and direction.

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

(5) work done

Answer:

work done is a scalar quantity, as it is the product of two vectors.

Question 4: In Fig 10.6 (a square), identify the following vectors.
(1) Coinitial

Answer:

Since vector $\vec{a}$ and vector $\vec{d}$ are starting from the same point, they are coinitial.

Question 4: In Fig 10.6 (a square), identify the following vectors.
(2) Equal

Answer:

Since Vector $\vec{b}$ and Vector $\vec{d}$ both have the same magnitude and same direction, they are equal.

Question 4: In Fig 10.6 (a square), identify the following vectors.

(3) Collinear but not equal

Answer:

Since vector $\vec{a}$ and vector $\vec{c}$ have the same magnitude but different direction, they are colinear and not equal.

Question 5: Answer the following as true or false.
(1) $\vec a$ and $-\vec a$ are collinear.

Answer:

True, $\vec a$ and $-\vec a$ are collinear. they both are parallel to one line hence they are colinear.

Question 5: Answer the following as true or false.
(2) Two collinear vectors are always equal in magnitude.

Answer:

False, because colinear means they are parallel to the same line but their magnitude can be anything and hence this is a false statement.

Question 5: Answer the following as true or false.

(3) Two vectors having same magnitude are collinear.

Answer:

False, because any two non-colinear vectors can have the same magnitude.

Question 5: Answer the following as true or false.

(4) Two collinear vectors having the same magnitude are equal.

Answer:

False, because two collinear vectors with the same magnitude can have opposite direction