Chapter 7 Linear Programming Ex 7.3

Question 1.A manufacturing firm produces two types of gadgets A and B, which are first processed in the foundry and then sent to machine shop for finishing. The number of man hours of labour required in each shop for production of A and B per unit and the number of man hours available for the … Read more

Chapter 7 Linear Programming Ex 7.2

I) Find the feasible solution of the following inequations graphically.Question 1.3x + 2y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0Solution:First we draw the lines AB and CD whose equations are 3x + 2y = 18 and 2x + y = 10 respectively. The feasible solution is OCPBO which is … Read more

Chapter 7 Linear Programming Ex 7.1

Question 1.Solve graphically :(i) x ≥ 0Solution:Consider the line whose equation is x = 0. This represents the Y-axis.To find the solution set, we have to check any point other than origin.Let us check the point (1, 1)When x = 1, x ≥ 0∴ (1, 1) lies in the required regionTherefore, the solution set is … Read more

Chapter 6 Line and Plane Miscellaneous Exercise 6B

Question 1.Solution: Question 2.The vector equation of line 2x – 1 = 3y + 2 = z – 2 is Solution: Question 3.The direction ratios of the line which is perpendicular to the two lines  (A) 4, 5, 7(B) 4, -5, 7(C) 4, -5, -7(D) -4, 5, 8Solution:(A) 4, 5, 7 Question 4. Question 5. … Read more

Chapter 6 Line and Plane Miscellaneous Exercise 6A

Question 1. Question 2. Question 3. Question 4. Question 5.Find the vector equation of the line which passes through the origin and the point (5, -2, 3).Solution: Question 6.Find the Cartesian equations of the line which passes through points (3, -2, -5) and (3, -2, 6).Solution:Let A = (3, -2, -5), B = (3, -2, … Read more

Chapter 6 Line and Plane Ex 6.4

Question 1. Question 2. Question 3.Show that Solution: Question 4. Question 5.Find the distance of the point (1, 1, -1) from the plane 3x + 4y – 12z + 20 = 0.Solution:

Chapter 6 Line and Plane Ex 6.3

Question 1. Question 2.Find the perpendicular distance of the origin from the plane 6x – 2y + 3z – 7 = 0.Solution:Alternative Method:The equation of the plane is 6x – 2y + 3z – 7 = 0 i.e. 6x – 2y + 3z = 7This is the normal form of the equation of plane.∴ perpendicular … Read more

Chapter 6 Line and Plane Ex 6.2

Question 1.Solution:Let PM be the perpendicular drawn from the point P (2, -3, 1) to the line  The coordinates of any point on the line are given by x = -1 + 2λ, y = 3 + 3λ, z = -1 – λLet the coordinates of M be(-1 + 2λ, 3 + 3λ, -1 – … Read more

Chapter 6 Line and Plane Ex 6.1

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

Chapter 5 Vectors Miscellaneous Exercise 5

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