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1. Let l1 be the line determined by (2,1, 3) and (1, 2 - 1) and let l2 be the line determined by (0, 2, 3) and (-1,1, 2) . Is l1 parallel to l2 ? Explain your answer. 2. Prove that for any two vectors u and v in R2 or R3 , u + v 2 + u - v 2 = 2 u 2 + 2 v 2 . 3. Find the parametric equations of the line through the origin that is perpendicular to both u=(-1,2,3) and v=(2,0,1/2). 4. Find the distance from the point P(1,-1,1) to the line x(t) = (0,2,1) + t(1,1,1), and the closest point on the line to point P . 5. Showthatthethreeplanes x+y+z=2, -x-y+4z=3 and x+y+2z=3 intersectin a line, and find the equation of that line.
Which job should you take? After completing your degree you have a choice between 2 jobs suppose that you do not have a preference in location and have been given the following offer.
A jeweler needs to mix an alloy with 14% gold content and an alloy with a 24% gold content to obtain 50 ounces of a new alloy with exactly 20% gold content. How many ounces of each of the original alloys must be used? [Round to the nearest tenth o..
paste match sticks above for doding and answer on the three vertices of triangle. you will find number of small triangles in the spectacular triangle.
Find the probability of selecting an eight, A card is selected from a standard deck of 52 playing cards. Find the probability of selecting
Water is pumped out of a holding tank at a rate of 6- 6e-0.10t liters/minute, where t is in minutes since the pump is started. If the holding tank contains 1000 liters of water when the pump is started, how much water does it hold one hour later?
A motorboat travels 455 km in 7 hours going upstream and 963 km in 9 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
how many bicycles must be produced each day for the average cost to be no more than $100?
let s be the solid obtained by intersecting two cylinders of radius r whose axes intersect at an angle theta. find the volume of S as a function of r and theta.
Find the mass and center of masss of the solid S bounded by the paraboloid z= 4x^2 + 4y^2 and the plane z= a (a is greater than 0) if S has constant density K.
Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 mioles per hour
a stockholder sold 150 shares of stock at 34 1/4 per share find the stockholders loss per share The stock had been purchased at 36 5/8 per share.
Last season, a pair of jeans cost $44.95. This season, the price of the jeans increased by 15 percent. Later in the season, the jeans were put on sale for 15 percent off.
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