PSEB 12th Class Maths Solutions Chapter 10 Vector Algebra Ex 10.1

Punjab State Board PSEB 12th Class Maths Book Solutions Chapter 10 Vector Algebra Ex 10.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.1

Question 1.
Represent graphically a displacement of 40 km, 30° east of north.
Solution.
The displacement is 30° east of north so, we have to draw a straight line making 30° with north.

Here, vector \(\overrightarrow{O P}\) represents the displacement of 40 km, 30° east of north.

Question 2.
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/sec²
Solution.
(i) 10 kg is a scalar quantity because it involves only magnitude.
(ii) 2 metres north-west is a vector quantity as it involves both magnitude and direction.
(iii) 40° is a scalar quantity as it involves only magnitude.
(iv) 40 watts is a scalar quantity as it involves only magnitude.
(v) 10^{– 19} coulomb is a scalar quantity as it involves only magnitude.
(vi) 20 m/sec² is a vector quantity as it involves magnitude as well as direction.

Question 3.
Classify the following as scalar and vector quantities.
(i) time period
(ii) distance
(iii) force
(iv) velocity
(v) work done
Solution.
(i) Time period is a scalar quantity as it involves only magnitude.
(ii) Distance is a scalar quantity as it involves only magnitude.
(iii) Force is a vector quantity as it involves both magnitude and direction.
(iv) Velocity is a vector quantity as it involves both magnitude as well as direction.
(v) Work done is a scalar quantity as it involves only magnitude.

Question 4.
In Figure, (a square) identify the following vectors.
(i) Coinitial
(ii) Equal
(iii) Collinear but not equal
Solution.

(i) Vectors \(\vec{a}\) and \(\vec{d}\) are coinitial because they have the same initial point.
(ii) Vectors \(\vec{b}\) and \(\vec{d}\) are equal because they have the same magnitude and direction.
(iii) Vectors \(\vec{a}\) and \(\vec{c}\) are collinear but not equal. This is because although they are parallel, their directions are not the same.

Question 5.
Answer the following as true or false.
(i) \(\vec{a}\) and – \(\vec{a}\) are collinear.
Solution.
True

(ii) Two collinear vectors are always equal in magnitude.
Solution.
False

(iii) Two vectors having same magnitude are collinear.
Solution.
False

(iv) Two collinear vectors having the same magnitude are equal.
Solution.
False.