NCERT Solutions for Class 12 Mathemetics Chapter 10 - Vector Algebra

Question 1:

Represent graphically a 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-east
(iii) 40$°$ (iv) 40 watt
(v) 10^–19 coulombs (vi) 20 m/s².

Question 3:

(i) Scalar (ii) Scalar
(iii) Vector (iv) Vector
(v) Scalar.

Question 4:

Question 5:

1. TRUE
2. FALSE

Question 6:

The collinear vectors are always equal in magnitude.

1. TRUE
2. FALSE

Question 7:

Two vectors having same magnitudes are collinear.

1. TRUE
2. FALSE

Question 8:

The collinear vectors having the same magnitude are equal.

1. TRUE
2. FALSE

Question 9:

Question 10:

Write two different vectors having same magnitude.

Question 11:

Write two different vectors having the same direction.

Question 12:

Question 13:

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

Question 14:

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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.

Question 22:

Question 23:

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).

Question 25:

Question 26:

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

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Question 45:

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

4. 

Question 46:

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Question 57:

1. 

2. 1
3. 2
4. 4

Question 58:

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Question 61:

Question 62:

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 64:

Question 65:

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

Question 66:

Question 67:

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

4. 

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 = $\mathrm{\lambda }$.

Question 69:

Question 70:

1. 

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

Question 71:

1. 

2. 

3. 0 < $\mathrm{\theta }$ < $\mathrm{\pi }$
4. 0 ≤ $\mathrm{\theta }$ ≤ $\mathrm{\pi }$

Question 72:

Question 73:

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

Question 74:

1. 0

2. 

3. 

4. $\mathrm{\pi }$

Question 75:

1. 

2. 42

3. 

4.