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.
The equation of the line 5x-25 =14-7y =35z can be rewritten as
Since the required line is parallel to the given line, so the direction ratio of the required line is proportional to 7,-5,1
The vector equation of the required line passing through the point (1,2-1) and having direction ratios proportional to 7,-5 1 is
Prove that if E and F are independent events, then the events E and F' are also independent.
A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ` 100 and that on a bracelet is ` 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.