# NCERT Solutions for Class 12 Mathemetics Chapter 10 - Vector Algebra

##### Question 1:

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

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$°$ (iv) 40 watt
(v) 10–19 coulombs (vi) 20 m/s2.

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.

In the figure, (square) identify the following vectors :
(i) Co-initial (ii) Equal
(iii) Collinear but not equal.

1. TRUE
2. FALSE

TRUE

##### Question 6:

The collinear vectors are always equal in magnitude.

1. TRUE
2. FALSE

FALSE

##### Question 7:

Two vectors having same magnitudes are collinear.

1. TRUE
2. FALSE

FALSE

##### Question 8:

The collinear vectors having the same magnitude are equal.

1. TRUE
2. FALSE

TRUE

##### Question 10:

Write two different vectors having same magnitude.

##### Question 11:

Write two different vectors having the same direction.

##### Question 13:

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

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

##### 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.

Vector joining the points A and B

##### 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).

Mid-point of the vector joining the points

##### Question 26:

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

##### Question 45:

1. $\mathrm{\lambda }$ = 1
2. $\mathrm{\lambda }$ = – 1
3. a = | $\mathrm{\lambda }$ |

1. 1
2. 2
3. 4

2

##### Question 62:

if –2(1 + 6) + 4(1 + 4) – 6(3 – 2) = 0
if –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.

##### Question 65:

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

##### Question 67:

1. $\mathrm{\lambda }$ = 1
2. $\mathrm{\lambda }$ = – 1
3. a = | $\mathrm{\lambda }$ |

##### Question 68:

1. x = 2$\mathrm{\lambda }$, y = $\mathrm{\lambda }$, z = $\mathrm{\lambda }$
2. x = $\mathrm{\lambda }$, y = 2$\mathrm{\lambda }$, z = – $\mathrm{\lambda }$
3. x = –$\mathrm{\lambda }$, y = 2$\mathrm{\lambda }$, z = $\mathrm{\lambda }$
4. x = – $\mathrm{\lambda }$, y = – 2$\mathrm{\lambda }$, z = $\mathrm{\lambda }$.

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

##### Question 70:

1. 1 square unit
2. 2 square units
3. 4 square units

2 square units

##### Question 71:

1. 0 < $\mathrm{\theta }$ < $\mathrm{\pi }$
2. 0 ≤ $\mathrm{\theta }$$\mathrm{\pi }$

1. 0
2. -1
3. 1
4. 3

3

##### Question 74:

1. 0
2. $\mathrm{\pi }$

1. 42