RD SHARMA SOLUTION CHAPTER- 28 The Straight Line in Space I CLASS 12TH MATHEMATICS-EDUGROWN

Chapter 28 Straight line in space Exercise Ex. 28.1

Question 1

Solution 1

Question 2

Find the vector equation of the line passing through the points (-1, 0, 2) and (3, 4, 6).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

Chapter 28 Straight line in space Exercise Ex. 28.2

Question 1

Solution 1

Question 2

Show that the line through the points (1, -1, 2) and (3, 4, -2) is perpendicular to the line through points (0, 3, 2) and (3, 5, 6).Solution 2

Question 3

Show that the line through the points (4, 7, 8) and (2, 3, 4) is parallel to the line through the points (-1, -2, 1) and (1, 2, 5).Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, -1) and (4, 3, -1).Solution 6

Question 7

Find the equation of a line parallel to x-axis and passing through the origin.Solution 7

Question 8(i)

Solution 8(i)

Question 8(ii)

Solution 8(ii)

Question 8(iii)

Solution 8(iii)

Question 9(i)

Solution 9(i)

Question 9(ii)

Solution 9(ii)

Question 9(iii)

Solution 9(iii)

Question 9(iv)

Solution 9(iv)

Question 9(v)

Solution 9(v)

Question 9(vi)

find the angle between the following pairs of line :

Solution 9(vi)

Question 10(i)

Solution 10(i)

Question 10(ii)

Solution 10(ii)

Question 10(iii)

Solution 10(iii)

Question 10(iv)

find the angle between the pairs of lines with directions ratios proposal to a, b, c and b – c, c – a, a – b.Solution 10(iv)

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

Chapter 28 Straight line in space Exercise Ex. 28.3

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6(i)

Solution 6(i)

Question 6(ii)

Solution 6(ii)

Question 6(iii)

Solution 6(iii)

Question 6(iv)

Solution 6(iv)

Question 7

Solution 7

Chapter 28 Straight line in space Exercise Ex. 28.4

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

..Question 4

Solution 4

Question 5

Find the foot of perpendicular from the point (2, 3, 4) to the line . Also find the perpendicular distance from the given point to the line.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 coordinates of the foot of perpendicular drawn from the point A (1, 8, 4) to the line joining the points B (0, -1, 3) and C (2, -3, -1).Solution 14

Chapter 28 Straight line in space Exercise Ex. 28.5

Question 1(i)

Find the shortest distance between the pair of lines whose vector equation are

Solution 1(i)

Question 1(ii)

Find the shortest distance between the pair of lines whose vector equations are:

Solution 1(ii)

Question 1(iii)

Find the shortest distance between the pair of lines whose vector equations are:

Solution 1(iii)

Question 1(iv)

Find the shortest distance between the lines whose vector equations are:

Solution 1(iv)

Question 1(v)

Find the shortest distance between the pair of lines whose vector equations are:

Solution 1(v)

Question 1(vi)

Find the shortest distance between the pair of lines whose vector equations are:

Solution 1(vi)

Question 1(vii)

Solution 1(vii)

Question 1(viii)

Solution 1(viii)

Question 2(i)

Find the shortest distance between the pair of lines whose cartesian equations are:

.Solution 2(i)

Question 2(ii)

Find the shortest distance between the pair of lines whose cartesian equations are:

.Solution 2(ii)

Question 2(iii)

Find the shortest distance between the pair of lines whose cartesian equations are:

.Solution 2(iii)

Question 2(iv)

Find the shortest distance between the pair of lines whose Cartesian equations are:

.Solution 2(iv)

Question 3(i)

Solution 3(i)

Question 3(ii)

Solution 3(ii)

Question 3(iii)

Solution 3(iii)

Question 3(iv)

Solution 3(iv)

Question 4(i)

Solution 4(i)

Question 4(ii)

Solution 4(ii)

Question 5

Solution 5

Question 6

Solution 6

Question 7(i)

Find the shortest distance between the lines

Solution 7(i)

Question 7(ii)

Find the shortest distance between the lines

Solution 7(ii)

Question 7(iii)

Find the shortest distance between the lines

Solution 7(iii)

Question 7(iv)

Find the shortest distance between the lines

Solution 7(iv)

Question 8

Find the distance between the lines l₁ and l₂ given by

Solution 8