Table of Contents
Chapter 29 The plane Exercise Ex. 29.1
Question 1(i)
Solution 1(i)
Question 1(ii)
Solution 1(ii)
Question 1(iii)
Solution 1(iii)
Question 1(iv)
Solution 1(iv)
Question 1(v)
Solution 1(v)
Question 2
Solution 2
Question 3(i)
Solution 3(i)
Question 3(ii)
Solution 3(ii)
Chapter 29 The plane Exercise Ex. 29.2
Question 1
Solution 1
Question 2(i)
Solution 2(i)
Question 2(ii)
Solution 2(ii)
Question 2(iii)
Solution 2(iii)
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Chapter 29 The plane Exercise Ex. 29.3
Question 1
Solution 1
Question 2(i)
Solution 2(i)
Question 2(ii)
Solution 2(ii)
Question 3
Solution 3
Question 4(i)
Solution 4(i)
Question 4(ii)
Solution 4(ii)
Question 4(iii)
Solution 4(iii)
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(i)
Solution 13(i)
Question 13(ii)
Solution 13(ii)
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Find the vector and Cartesian equations of the plane which passes through the point (5, 2, -4) and perpendicular to the line with direction ratios 2, 3, -1.Solution 18
Question 19
If O be the origin and the coordinates of P be (1, 2, -3), then find the equation of the plane passing through P and perpendicular to OP.Solution 19
Question 20
If O is the origin and the coordinates of A are (a, b, c). Find the direction cosines of OA and the equation of the plane through A at right angles to OA.Solution 20
Chapter 29 The plane Exercise Ex. 29.4
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
Find the distance of the plane 2x – 3y + 4z – 6 = 0 from the origin.Solution 11
Chapter 29 The plane Exercise Ex. 29.5
Question 1
Solution 1
Question 2
Find the vector equation of the plane passing through the points P(2, 5, -3), Q(-2, -3, 5) and R(5, 3, -3).Solution 2
Question 3
Solution 3
Question 4
Find the vector equation of the plane passing through the points (1, 1, -1), (6, 4, -5) and (-4, -2, 3).Solution 4
Question 5
Solution 5
Chapter 29 The plane Exercise Ex. 29.6
Question 1(i)
Solution 1(i)
Question 1(ii)
Solution 1(ii)
Question 1(iii)
Solution 1(iii)
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 2(v)
Find the angle between the planes:
2x + y – 2z = 5 and 3x – 6y – 2z = 7Solution 2(v)
Question 3(i)
Solution 3(i)
Question 3(ii)
Solution 3(ii)
Question 4(i)
Solution 4(i)
Question 4(ii)
Solution 4(ii)
Question 4(iii)
Solution 4(iii)
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
Find the equation of the plane with intercept 3 on the y-axis and parallel to ZOX plane.Solution 11
Question 12
Find the equation of the plane that contains the point (1, -1, 2) and is perpendicular to each of the planes 2x + 3y – 2z = 5 and x + 2y – 3z = 8.Solution 12
Question 13
Solution 13
Question 14
Find the equation of the plane passing through the point (-1, 3, 2) and perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0.Solution 14
Question 15
Find the vector equation of the plane through the points (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane x – 2y + 4z = 10.Solution 15
Chapter 29 The plane Exercise Ex. 29.7
Question 1(i)
Solution 1(i)
Question 1(ii)
Solution 1(ii)
Question 1(iii)
Solution 1(iii)
Question 1(iv)
Solution 1(iv)
Question 2(i)
Solution 2(i)
Question 2(ii)
Solution 2(ii)
Question 3(i)
Solution 3(i)
Question 3(ii)
Solution 3(ii)
Chapter 29 The plane Exercise Ex. 29.8
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
Find the equation of the plane through the intersection of the planes 3x – y 2z = 4 and x + y + z = 2 and the point (2, 2, 1).Solution 15
Question 16
Find the vector equation of the plane through the line of intersection of the plane x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0.Solution 16
Question 17
Find the equation of the plane passing through (a, b, c) and parallel to the plane
Solution 17
Chapter 29 The plane Exercise Ex. 29.9
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
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Find the distance between the point (7, 2, 4) and the plane determined by the points A (2, 5, -3), B (-2, -3, 5) and C (5, 3, -3)Solution 11
Question 12
A plane makes intercepts -6, 3, 4 respectively on the coordinate axes. Find the length of the perpendicular from the origin on it.Solution 12
Chapter 29 The plane Exercise Ex. 29.10
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Chapter 29 The plane Exercise Ex. 29.11
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
Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25
Find the equation of the plane passing through the points
(-1, 2, 0),(2, 2, -1) and parallel to the line
Solution 25
Chapter 29 The plane Exercise Ex. 29.12
Question 1(i)
Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the yz-plane.Solution 1(i)
Question 1(ii)
Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the zx-plane.Solution 1(ii)
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Find the distance of the point P (-1, -5, -10) from the point of intersection of the line joining the points A (2, -1, 2) and B (5, 3, 4) with the plane x – y + z = 5.Solution 5
Question 6
Find the distance of the point P(3, 4,4) from the point, where the line joining the points A(3, -4, -5) and B (2, -3, 1) intersects the plane 2x + y + z =7.Solution 6
Chapter 29 The plane Exercise Ex. 29.13
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
Find the equation of a plane which passes through the point (3, 2, 0) and contains the line
Solution 13
Chapter 29 The plane Exercise Ex. 29.14
Question 1
Solution 1
Question 2
Solution 2
Question 3
Find the shortest distance between the lines
Solution 3
Chapter 29 The plane Exercise Ex. 29.15
Question 1
Solution 1
Question 2
Solution 2
Question 3
Hence or otherwise deduce the length of the perpendicular.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
Find the length and the foot of perpendicular from the point (1, 3/2, 2) to the plane 2x – 2y + 4z + 5 = 0.Solution 14
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