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In Problems 39 and 40, show that the given lines intersect and find the acute angle between
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Chapter 3 Solutions
Mathematical Methods in the Physical Sciences
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- For the 30-60-90 triangle shown, suppose that XY=2a. Find: a XZ b YZarrow_forward(3) Let I be a line and P be a point not on I. Construct lines l, and l2 through P such that l, meets I at 45° and l2 meets at l at 30°. (You can use the sum of the angles inside a triangle is 180° in this problem.)arrow_forward14. Find MZSTV. R (9x + 1)° -(23r-7)° U Sarrow_forward
- Let = -2- 4 + 5 K, and V u = −2+ 4-5k, Calculate , ull, (the angle between (2 decimal places) lull = • ull, and e and u in degrees) ||| ll = . 0 = lo -6arrow_forward4. Given that A(1, 1, – 3), B(5, 4, – 1) and C(2, – 1, – 5) are three points in the 3-dimensional coordinate system with O as the origin. (a) D is a point on the line segment AB such that AD : DB = 3 : 4, find the coordinates of D. (b) Find AB and AC. (c) Find AB · AC. (d) Find AB × AC. (e) Find two unit vectors which are perpendicular to both AB and AC.arrow_forward10. Suppose we have the following lines: 4:x=-3+31, y =1+1, z = -4+4t L :x =-1+s, y = 3–2s, z =1+2s Show that these lines are skew. Find the distance between these lines. Can you find the points C and D, that are points on L, and L, respectively, such that the distance between C and D is the same as the distance between the lines?arrow_forward
- 15. Find the Cartesian equation of the following lines: a. parallel to the line r= 2i+3j+ 4k +t(3i- j+2k) and passes through (1, –2, –3); b. passes through (2,6,–1) and in the direction i– 2k.arrow_forward3. A woman launches a boat from one shore of a straight river and wants to land at the point directly opposite on the other side/shore. If the speed of the boat (in still water) is 16 mph and the river is flowing east at the rate of 8 mph in what direction should she head the boat in order to arrive at the desired landing point? (direction is the angle)arrow_forwardIf W = 2x 2 + 3xy2 - 20y-2+ 6u; where x = 5u2 +4v 2 and y= u - 4v3 , find §W / §V.arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
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