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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.
She plans to use a stratified sampling method in which of the total population is included in the studies. How many yellow perch will be in her sample?
A baseball diamond is a square 90 feet on a side. A player is running from second base to third base at the rate of 15 feet per second. Find the rate of change of the distance from the player to home plate at the instant the player is 10 feet from..
You are experimenting with designs for a fruit bowl with a square base. The general idea is to attach congruent regular polygons to the sides of the base and "fold them up" until the closest edges of adjacent polygons meet.
A building is 479 feet tall. For a class project, Kari is to make a scale model of the building to place in the front hall display case. The display case is 21 inches tall. Which scale will allow her to make the tallest model that will fit in the ..
A restaurant sells ice cream and frozen yogurt. The restaurant makes one order for ice cream and frozen yogurt per week, and the store has enough freezer space for 110 gallons of both products
How much should he invest in each to maximize his return? Assume the investment returns are as expected.
Starting with a hypothetical population of 14,000 people and an even age distribution [1,000 in each age group from 1-5 to 66-70 years], suppose that the population initially has a total fertility rate of 2.0 and an average life span of 70 years.
College officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. How many randomly selected students must be surveyed in order to be 95% confident that the sample percentage has a margin of error of 2 per..
A tank in the shape of a sphere with radius 10 m is full of gasoline, with density 680 kg/m3. Calculate the work required to empty the tank through a hole at the top.
Let G be the group of symmetries of a cube, including the orientation-reversing symmetries. Describe the elements of G geometrically.
A gun has a muzzle speed of 100 meters per second. What angle of elevation should be used to hit an object 190 meters away? Neglect air resistance and use as the acceleration of gravity.
Find the values of the trigonometric functions of t from the given information.
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