Table of Contents
Chapter 23 Algebra of Vectors Exercise Ex. 23.1
Question 1(i)
Represent graphically a dispacement of 40 km, 30° east of north.Solution 1(i)
Question 1(ii)
Represent graphically a displacement of 50 km, south-eastSolution 1(ii)
Here, vector represents the displacement of 50 km, south-east.Question 1(iii)
Represent graphically a displacement of 70 km, 40° north of west.Solution 1(iii)
Here, vector represents the displacement of 70 km, 40° north of west.Question 2
Classify the following measures as scalars and vectors.
(i) 15 kg
(ii) 20 kg weight
(iii) 45°
(iv) 10 metres south-east
(v) 50 m/s2Solution 2
(i) 15 kg is a scalar quantity because it involves only
(ii) 20 kg weight is a vector quantity as it involves both magnitude and direction.
(iii) 45° is a scalar quantity as it involves only magnitude.
(iv) 10 metres south-east is a vector quantity as it involve direction.
(v) 50 m/s2 is a scalar quantity as it involves magnitude of acceleration.Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Chapter 23 Algebra of Vectors Exercise Ex. 23.2
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Chapter 23 Algebra of Vectors Exercise Ex. 23.3
Question 1
Find the position vector of a point R which divides the line joining the two points P and Q with position vectors
Solution 1
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Chapter 23 – Algebra of Vectors Exercise Ex. 23.4
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Prove by vector method that the internal bisectors of the angles of a triangle are concurrent.Solution 6
Chapter 23 – Algebra of Vectors Exercise Ex. 23.5
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Find |AB| in each case.Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 12
Solution 12
Chapter 23 Algebra of Vectors Exercise Ex. 23.6
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Chapter 23 Algebra of Vectors Exercise Ex. 23.7
Question 1
Solution 1
Question 2 (i)
Solution 2 (i)
Question 2 (ii)
Solution 2 (ii)
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Using vectors, find the value of λ such that the points
(λ, – 10, 3), (1 -1, 3) and (3, 5, 3) are collinear.Solution 13
Chapter 23 Algebra of Vectors Exercise Ex. 23.8
Question 1
Solution 1
Question 2 (i)
Solution 2 (i)
Question 2 (ii)
Solution 2 (ii)
Question 2 (iii)
Solution 2 (iii)
Question 2 (iv)
Solution 2 (iv)
Question 3 (i)
Solution 3 (i)
Question 3 (ii)
Solution 3 (ii)
Question 4
Solution 4
Question 5 (i)
Solution 5 (i)
Question 5 (ii)
Solution 5 (ii)
Question 6 (i)
Solution 6 (i)
Question 6 (ii)
Solution 6 (ii)
Question 7 (i)
Solution 7 (i)
Question 7 (ii)
Solution 7 (ii)
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Chapter 23 Algebra of Vectors Exercise Ex. 23.9
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7 (i)
Solution 7 (i)
Question 7 (ii)
Solution 7 (ii)
Question 7 (iii)
Solution 7 (iii)
Question 8
Solution 8
Question 9
Solution 9
Question 10
If a unit vector makes and angles and an acute angle θ with , then find θ and hence, the components of .Solution 10
Question 11
Solution 11
Question 12
Solution 12
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