GSEB Solutions Class 12 Maths Chapter 10 Vector Algebra Ex 10.1

Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 10 Vector Algebra Ex 10.1 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 12 Maths Chapter 10 Vector Algebra Ex 10.1

Question 1.
Represent graphically a displacement of 40 km, 30° east of north.
Solution:
A line segment of 2 cm is drawn on the right of OY making an angle of 30° with it.
OP = 40 km, scale 1 cm = 20 km.
Vector \(\overline{\mathrm{OP}}\) represents 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^-10 columb
(vi) 20 m/sec²
Solution:
Scalars:
(i) 10 kg
(iii) 40°
(iv) 40 watt
(v) 10^-10 columb

Vectors:
(ii) 2 metres north-west
(vi) 20 m/sec²

Question 3.
Classify the following as scalar and vector quantities:
(i) time period
(ii) distance
(iii) force
(iv) velocity
(v) work
Solution:
Scalar Quantity:
(i) time
(ii) distance
(v) work

Vector Quantity:
(iii) force
(iv) velocity

Question 4.
In a square, identify the following vectors:
(i) co-initial
(ii) equal
(iii) collinear but not equal
Solution:
(i) Coinitial vectors are \(\vec{a}\) and \(\vec{d}\).
(ii) Equal vectors are \(\vec{b}\) and \(\vec{d}\).
(iii) Collinear but not equal vectors are \(\vec{a}\) and \(\vec{c}\).

Question 5.
Answer the following as true and false:
(i) \(\vec{a}\) and – \(\vec{a}\) are collinear.
(ii) Two collinear vectors are always equal in magnitude.
(iii) Two vectors having the same magnitude are collinear.
(iv) Two collinear vectors having same magnitude are equal.
Solution:
(i) True
(ii) False
(iii) False
(iv) False.