##### Question 1:

Represent graphically a displacement of 40 km 30$\xb0$ east of north.

##### Answer:

Draw a line segment of length 4 cm on the right of ON, making an angle of 30° with ON, where

Scale : 1 cm = 10 km.

##### Question 2:

Classify the following measures as scalars and vectors :

(i) 10 kg

(ii) 2 metres north-east

(iii) 40$\xb0$ (iv) 40 watt

(v) 10^{–19} coulombs (vi) 20 m/s^{2}.

##### Answer:

Classify the following as scalar and vector quantities :

(i) time period (ii) distance

(iii) force (iv) velocity

(v) work-done.

##### Question 3:

(i) Scalar (ii) Scalar

(iii) Vector (iv) Vector

(v) Scalar.

##### Answer:

In the figure, (square) identify the following vectors :

(i) Co-initial (ii) Equal

(iii) Collinear but not equal.

##### Question 4:

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##### Question 5:

- TRUE
- FALSE

##### Answer:

TRUE

##### Question 6:

The collinear vectors are always equal in magnitude.

- TRUE
- FALSE

##### Answer:

FALSE

##### Question 7:

Two vectors having same magnitudes are collinear.

- TRUE
- FALSE

##### Answer:

FALSE

##### Question 8:

The collinear vectors having the same magnitude are equal.

- TRUE
- FALSE

##### Answer:

TRUE

##### Question 9:

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##### Question 10:

Write two different vectors having same magnitude.

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##### Question 11:

Write two different vectors having the same direction.

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##### Question 13:

Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7).

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Let A (2, 1) be the initial point and B (– 5, 7) the terminal point.

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##### Question 21:

Find the direction – cosines of the vector joining the points A (1, 2, – 3) and B (– 1, – 2, 1) directed from A to B.

##### Answer:

Vector joining the points A and B

##### Question 22:

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##### Question 24:

Find the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q (4, 1, – 2).

##### Answer:

Mid-point of the vector joining the points

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##### Question 26:

In triangle ABC (see Fig), which of the following is not true ?

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##### Question 45:

- $\mathrm{\lambda}$ = 1
- $\mathrm{\lambda}$ = – 1
- a = | $\mathrm{\lambda}$ |

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- 1
- 2
- 4

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2

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if –2(1 + 6) + 4(1 + 4) – 6(3 – 2) = 0if –14 + 20 – 6 = 0, which is true.

##### Question 63:

Find x such that the four points:

A(3, 2, 1), B(4, x, 5), C(4, 2, –2) and D(6, 5, –1) are coplaner.

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##### Question 65:

In $\u2206$ ABC, which of the following is not true ?

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##### Question 67:

- $\mathrm{\lambda}$ = 1
- $\mathrm{\lambda}$ = – 1
- a = | $\mathrm{\lambda}$ |

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##### Question 68:

- x = 2$\mathrm{\lambda}$, y = $\mathrm{\lambda}$, z = $\mathrm{\lambda}$
- x = $\mathrm{\lambda}$, y = 2$\mathrm{\lambda}$, z = – $\mathrm{\lambda}$
- x = –$\mathrm{\lambda}$, y = 2$\mathrm{\lambda}$, z = $\mathrm{\lambda}$
- x = – $\mathrm{\lambda}$, y = – 2$\mathrm{\lambda}$, z = $\mathrm{\lambda}$.

##### Answer:

x = –$\mathrm{\lambda}$, y = 2$\mathrm{\lambda}$, z = $\mathrm{\lambda}$

##### Question 69:

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##### Question 70:

- 1 square unit
- 2 square units
- 4 square units

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2 square units

##### Question 71:

- 0 < $\mathrm{\theta}$ < $\mathrm{\pi}$
- 0 ≤ $\mathrm{\theta}$ ≤ $\mathrm{\pi}$

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##### Question 73:

- 0
- -1
- 1
- 3

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3

##### Question 74:

- 0
- $\mathrm{\pi}$

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##### Question 75:

- 42