Sujeet Kumar

Question 1. Question 2. Question 3. Question 4. Solution: Question 5. Question 6.Find the Cartesian equations of the line passing through A(-1, 2, 1) and having direction ratios 2, 3, 1.Solution:The cartesian equations of the line passing through (x1, y1, z1) and having direction ratios a, b, c are∴ the cartesian equations of the line … Read more

I) Select the correct option from the given alternatives :Question 1.(A) 24(B) -24(C) 0(D) 48Solution:(C) 0 Question 2.Solution: Question 3.If sum of two unit vectors is itself a unit vector, then the magnitude of their difference is(A) √2(B) √3(C) 1(D) 2Solution:(B) √3 Question 4. Solution: Question 5.The volume of tetrahedron whose vertices are (1, -6, 10), (-1, -3, … Read more

Question 1. Question 2.Solution:= 3(8 + 3) – 0(16 + 9) + 5(4 – 6)= 33 – 0 – 10 = 23= 23 cubic units. Question 3. Solution:∴ -3(0 + 2p) – 4(0 – 2) – 2(-p – 0) = 0∴ -6p + 8 + 2p = 0∴ -4p = -8P = 2. Question 4.Prove … Read more

Question 1.Solution: Question 2. Question 3.∴ θ = 60°. Question 4.∴ unit vectors perpendicular to both the vectors a¯ and b¯. Question 6. Solution: Question 7. Question 8. Question 9. Question 10.Find the area of parallelogram whose diagonals are determined by the  Question 11. Question 12.By equality of vectors,z – y = 0 ….(2)x – z = 1 … Read more

Question 1. Question 2.∴ LHS = RHSHence, (a¯ + b¯)2 = (a¯ – b¯)2. Question 3.∴ c < 0.Hence, the angle between a and b is obtuse if c < 0. Question 4. Question 5.Suppose that all sides of a quadrilateral are equal in length and opposite sides are parallel. Use vector methods to show that the diagonals are perpendicular.Solution: … Read more

Question 1. (ii) externally.Solution:If R(r¯) divides the line segment joining P and Q externally in the ratio 3 : 2, by section formula for external division,∴ coordinates of R = (-19, 8, -21). Question 2.Find the position vector of midpoint M joining the points L (7, -6, 12) and N (5, 4, -2).Solution:∴ coordinates of … Read more

Question 1.Solution: Question 3. Solution: Question 4.If ABCDEF is a regular hexagon, show Solution:ABCDEF is a regular hexagon.∴ by the triangle law of addition of vectors, Question 5. Question 6. Solution: Question 7.Find the distance from (4, -2, 6) to each of the following :(a) The XY-planeSolution:Let the point A be (4, -2, 6).Then,The distance of … Read more

I : Choose correct alternatives.Question 1.If the equation 4×2 + hxy + y2 = 0 represents two coincident lines, then h = _________.(A) ± 2(B) ± 3(C) ± 4(D) ± 5Solution:(C) ± 4 Question 2.If the lines represented by kx2 – 3xy + 6y2 = 0 are perpendicular to each other then _________.(A) k = 6(B) k = -6(C) … Read more

Question 1.Find the joint equation of the pair of lines:(i) Through the point (2, -1) and parallel to lines represented by 2×2 + 3xy – 9y2 = 0Solution:The combined equation of the given lines is2x2 + 3 xy – 9y2 = 0i.e. 2×2 + 6xy – 3xy – 9y2 = 0i.e. 2x(x + 3y) – 3y(x + 3y) = 0i.e. (x … Read more

Question 1.Show that lines represented by 3×2 – 4xy – 3y2 = 0 are perpendicular to each other.Solution:Comparing the equation 3×2 – 4 xy – 3y2 = 0 with ax2 + 2hxy + by2 = 0, we get, a = 3, 2h = -4, b = -3 Since a + b = 3 + (-3) = 0, the lines represented by … Read more