**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 30^{o} east of north.

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

**(a) 20 kg (b) 4 meters north – south (c) 80 ^{o}**

**(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 80^{o}, 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.