Find the value of p, so that the lines:
are perpendicular to each other. Also find the equations of a line passing through a point (3, 2, -4) and parallel to line l1.
Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x- y + z = 0. Also find the distance of the plane obtained above, from the origin.
A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of 80 on each piece of type A and 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?
Let x be the number of pieces manufactured of type A and y be the number of pieces manufactured of type B. Let us summarize the data given in the problem as follows:
Product | Time for Fabricating (in hours) | Time for Finishing (in hours) | Maximum labour hours available |
Type A | 9 | 1 | 180 |
Type B | 12 | 3 | 30 |
Maximum Profit (in Rupees) | 80 | 120 |
Points | Value of Z |
A(12, 6) | Z = 80 x 12 + 120 x 6 = Rs. 1680 |
B(0, 10) | Z = 80 x 0 +120 x 10 = Rs. 1200 |
C(20, 0) | Z = 80 x 20 + 120 x 0 = Rs.1600 |
Find the Cartesian equation of the line passes through the point (-2, 4, -5) and is parallel to the line
Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z.
Find the distance of the point (-1,-51-10) from the point of intersection of the line and the plane