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41. Find the value of A if the vectors i+ Aj+3k and-2i+j-4k arc parallel. uectors ii + 3k and 2i -

41. Find the value of A if the vectors i+ Aj+3k and-2i+j-4k arc parallel. uectors ii + 3k and 2i -

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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41. Find the value of a if the vectors i+2j+3k and-2i+j-4k arc parallcl. Find the arca of the paraticlogram whose adjacent sides are delermined hy the vectors i-j + 3k and 2i - 7j+k. Let u, v and ww he vectors. Ifu. (vxw) = 0, then the three vectors are ... 42. 43. 44. Find the triple product of the vectors u=21+3j-7k, vmi+2j+8k and 2=2i+2j+2k. Find the valucs of A if the triplc scalar product of the vectors x-2i +3j - 17k, y=i+2j+4 ¿k and z= A1 + 2j + 2k is 32. Determine the value of d ifu (-1. 2. 11). v(1. 2.3) and w(-3, 1. 5) arc coplanar. IrA= (h. 1) and B= (4.3). Evaluate the valucs of k that make the angle hetween vectors A and B equals. 45. 46. 17. % (30"). Let ABCD be a square. AC is a diagonal. If the conrdinatesof A and C arc (-3,8) and (7,-2) respectively, find the coordinates of B and D. 49. Determinç the polar coordinate of the points whose Cartesian coordinate is p (5,3). 48. 50. What is the Cartesian coordinates of the point in a planc with polar conrdinate A 4, 51. Compute the distance betwcen the points p(2, 4) and Q (7.3) 52. Calculate the shortest distance between the two pnints 3, and (5. ) 53. Find the shortest path between the point (4, -3) and the origin. 54. Find the shortcst distance betwcen (a, b) and (-a, -b) Find coordinates of the midpoint joining the points (1.1) and (4,5) Find the midpoint of the line joining the point (5,1) to the point (3.-1). 55. 56. 57. Calculate the length of the shortest distance between (4, and the point (4,6). 58. Find the distance betwcen (2.4) and (7,4)
Transcribed Image Text:41. Find the value of a if the vectors i+2j+3k and-2i+j-4k arc parallcl. Find the arca of the paraticlogram whose adjacent sides are delermined hy the vectors i-j + 3k and 2i - 7j+k. Let u, v and ww he vectors. Ifu. (vxw) = 0, then the three vectors are ... 42. 43. 44. Find the triple product of the vectors u=21+3j-7k, vmi+2j+8k and 2=2i+2j+2k. Find the valucs of A if the triplc scalar product of the vectors x-2i +3j - 17k, y=i+2j+4 ¿k and z= A1 + 2j + 2k is 32. Determine the value of d ifu (-1. 2. 11). v(1. 2.3) and w(-3, 1. 5) arc coplanar. IrA= (h. 1) and B= (4.3). Evaluate the valucs of k that make the angle hetween vectors A and B equals. 45. 46. 17. % (30"). Let ABCD be a square. AC is a diagonal. If the conrdinatesof A and C arc (-3,8) and (7,-2) respectively, find the coordinates of B and D. 49. Determinç the polar coordinate of the points whose Cartesian coordinate is p (5,3). 48. 50. What is the Cartesian coordinates of the point in a planc with polar conrdinate A 4, 51. Compute the distance betwcen the points p(2, 4) and Q (7.3) 52. Calculate the shortest distance between the two pnints 3, and (5. ) 53. Find the shortest path between the point (4, -3) and the origin. 54. Find the shortcst distance betwcen (a, b) and (-a, -b) Find coordinates of the midpoint joining the points (1.1) and (4,5) Find the midpoint of the line joining the point (5,1) to the point (3.-1). 55. 56. 57. Calculate the length of the shortest distance between (4, and the point (4,6). 58. Find the distance betwcen (2.4) and (7,4)
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