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, 30Â° east of north.

Solution:

A line segment of 2 cm is drawn on the right of OY making an angle of 30Â° with it.

OP = 40 km, scale 1 cm = 20 km.

Vector \(\overline{\mathrm{OP}}\) represents displacement of 40 km, 30Â° east of north.

Question 2.

Classify the following measures as scalars and vectors:

(i) 10 kg

(ii) 2 metres north-west

(iii) 40Â°

(iv) 40 watt

(v) 10^{-10} columb

(vi) 20 m/sec^{2}

Solution:

Scalars:

(i) 10 kg

(iii) 40Â°

(iv) 40 watt

(v) 10^{-10} columb

Vectors:

(ii) 2 metres north-west

(vi) 20 m/sec^{2}

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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.