ProblemsFor problems marked . refer to page 519 for a hint, clue, or answer.L1 Vector algebra 1*Given two vectors A = (21 - 3j + 76) and B= (sî + j + 2k) find:(a) A + B: (b) A -B; (c) A B. (d) A x B.%3D12 Vector algebra 2*Given two vectors A = (3i - 23 + 5k) and B = (61 - 73 + 4k) find:(a) A: (h) B: (c) (A B.13 Cosine and sine by vector algebra"Find the cosine and the sine of the angle between A = (31 + j+ k)and B = (-2i +j+ k).14 Direction cosinesThe direction cosines of a vector are the cosines of the angles itmakes with the coordinate axes. The cosines of the angles betweenthe vector and the x, y, and z axes are usually called, in turn., a.B.and y. Prove that a +B? +y = 1, using either geometry or vectoralgebra.15 Perpendicular vectorsShow that if A - Bj = |A + BỊ, then A and B are perpendicular.16 Diagonals of a parallelogramShow that the diagonals of an equilateral parallelogram areperpendicular.17 Law of sinesProve the law of sines using the cross product. It should only takea couple of lines.

Since you have posted a question with a multiple sub parts, we will solve first three sub - parts…

Answered: LI Vector algebra 1 Given two vectors A…

LI Vector algebra 1 Given two vectors A = (2i - 3j + T6) and B = (si +j+ 2k) find: (a) A+ B: (b) A- B: (c) A B: (d) A X B.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter3: Vectors

Section: Chapter Questions

Problem 65PQ

See similar textbooks

Similar questions

With respect to the following vectors: P = 9.73i - 7.36j + 1.02k; Q = - 1.77i - 3.68j + 1.43k, Answer the following questions: 10. What is the x-component of the unit vector joining vectors P and Q?11. What is the y-component of the unit vector joining vectors P and Q?12. What is the z-component of the unit vector joining vectors P and Q?13. Determine the projection of the vector P on the unit vector along PQ
The displacement vectors A and B shown in the figure below both have magnitudes of 3.70 m. The direction of vector A is ? = 22.0°. A graph shows two displacement vectors A and B plotted on an xy plane. Vector A is a straight diagonal line that starts from the zero point and extends into the first quadrant at an angle ? with the horizontal. Vector B starts from the zero point and extends up along the y-axis. (a) Find A + B graphically. magnitude m direction ° counterclockwise from the +x axis (b) Find A − B graphically. magnitude m direction ° counterclockwise from the +x axis (c) Find B − A graphically. magnitude m direction ° counterclockwise from the +x axis (d) Find A − 2B graphically. magnitude m direction ° counterclockwise from the +x axis
3. What is the volume of a parallelepiped whose edges are represented by A= 2i-3j+4k,B= i+2j-k, and C= 3i-j+2ka. 7 cubic units b. 8 cubic units c. 9 cubic units d.10cubic units4.A vector which is not a null is calleda. resultant vector c. proper vectorb. rectangular vector d. component vectors
1.Perform the following vector arithmetic. A=3ˆı+5ˆȷ+7kˆ B= ˆȷ−kˆ C=3ˆı−5kˆ (a) ∣A+B×C∣ (b) C⋅(B×A) (c) Construct a unit vector dˆ that is perpendicular to both A and C.
Two vectors ??⃗ and ??�⃗ in three dimensional space are expressed by their coordinates (2, 4, – 5) and (1, 2, 3) respectively. a) Write down the two vectors ??⃗ and ??�⃗ in unit vector notations. (1 mark) b) Find the angles which the vector ??⃗ = (2, 4, – 5) makes with the -x, +y and +z axes. (6 marks)c) Find the projection of the vector ??⃗ = (2, 3, 1) in the perpendicular direction to the vector ??�⃗ = (1, 2, 3). (3 marks)
Vector A is 30° below the x-axis. Vector B is 35° to the right of the negative y-axis. You will be asked to find the resultant, R = A + B. What is the direction of the resultant? Hint: Draw Rx and Ry tip-to-tail first, so that you know exactly which way R is going! Group of answer choices 41.2° below the x-axis 46.1° below the x-axis 43.9° below the x-axis 48.8° below the x-axis
Match the vector to its description. The vectors are given by their components in 3D space, that is by (x,y,z) In the x,y plane, 45° to the x- and y-axes A vector pointing straight up, in the z direction. A vector of length √5 A vector making an angle of 45° to all three axes A. (10,10,10) B. (1,1,0) C. (0,0,99) D. (0,1,2)
Q1: Locate the centroid (using a horizontal element) of the area under the curve x = ky? fromx = 0tox = a.Giving thatk = a/b3.
Vector A, vector B, and vector C are drawn to scale in the figure below. The vector Ais 5.3 meters long and points 56 degrees counterclockwise from the positive x-axis. The vector B is 4.0 meters long and points along the negative x-axis. The vector C is 2.8 meters long and points 53 degrees clockwise from the negative x-axis. 1. What are Ax and Ay, the x and y components of vector A? 2. What are Cx and Ay, the x and y components of vector C? 3. What are Rx and Ry, the x and y components of the resultant vector R =A +B+C?
Vector lies in the xy plane. Both of its components will be negative if it points from the origin into which quadrant? (a) the first quadrant (b) the second quadrant (c) the third quadrant (d) the fourth quadrant (e) the second or fourth quadrants
A rectangular parallelepiped has dimensions a, b, and c as shown in Figure P3.45. (a) Obtain a vector expression for the face diagonal vector R1. (b) What is the magnitude of this vector? (c) Notice that R1,ck, and R2 make a right triangle. Obtain a vector expression for the body diagonal vector R2.
Vector A has a magnitude of 4.50 m and makes an angle of 64.0 with the positive x axis. Vector B, with a magnitude equal to that of vector A, points along the negative y axis (Fig. P3.16). Graphically find the magnitude and direction of the resultant vector a. A+B, b. AB, c. BA, and d. 2AB.