Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Miscellaneous Exercise Question 1. Which of the following group is not direction cosines of a line : (a) 1,1,1 (b) 0,0, -1 (c)-1,0,0 (d)0,-1,0 Solution: Direction cosines of a line are proportional to direction ratio’s. Let a, b and c are direction ratio’s, then…
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Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.7 Question 1. Find the angle between the planes : Solution: Question 2. Find the angle between the planes : (i) x + y + 2z = 9 and 2x – y + z = 15 (ii) 2 x – y + z…
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Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.6 Question 1. Find the equation of the plane which is perpendicular to x-axis and that passes through the point (2,-1,3). Solution: Equation of plane passing through point (2,-1,3) a(x – 2) + b(y + 1) + c(z – 3) = 0 ∵…
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Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.5 Question 1. Find the shortest distance between the lines Solution: Question 2. Find the shortest distance between the lines Solution: Minimum distance between the lines Question 3. Find the shortest distance between the lines, whose vector equations are Solution: Question 4. Find…
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Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.4 Question 1. Show that the lines = = and = = z, intersects. Find their point of intersection. Solution: It is clear from above that both lines intersect each other and the coordinates of point of intersection are (-1, -1, -1). Question…
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Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.3 Question 1. Find the angle between the lines Solution: Question 2. Find the angle between the lines Solution: Question 3. Show that the line passes through the points (1,-1,2) and (3,4,-2) is perpendicular to the line passes through the points (0, 3,…
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Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.2 Question 1. Find the equation of the line which passes through the points (5, 7,9) and is parallel to the following axis : (i) A-axis (ii) F-axis (iii) Z-axis Solution: Let position vector of point (5, 7, 9) (i) The line parallel…
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Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.1 Question 1. Find the direction cosines of a line which makes equal angles with the coordinate axis. Solution: Let the line makes equal angle 0 with the coordinate axis. ∴ Direction cosines are l = cos θ, m = cos θ, n…
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Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.5 Question 1. Find the value of Solution: Question 2. Prove that Solution: Question 3. Evaluate the formula Solution: Question 4. For any vector , prove that: Solution: We know that Question 5. Prove that Solution: Question 6. Prove that ,,are coplanar if × ,…
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Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.4 Question 1. Prove that: Solution: Question 2. Solution: Question 3. Prove that vectors and are coplanar Solution: Question 4. For which value of λ, following vectors are coplanar : Solution: Question 5. Prove that the following four points are coplanar: (i) A(- 1,4,-3), B(3,2,-5),…
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