A rectangular cantilever beam AB has point A positioned at the origin of the coordinate system and point B at coordinates (1.2, -0.3, 2.4) m. The vector ₁ = (1î + 123 + 1ê) m is oriented parallel to the thin cross-sectional dimension, and is perpendicular to to FAB (directed along the beam axis AB).
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- Given vector A = <10, 20, 18> and vector B = <16, -17, -24> , what is A dot B?Q1) Given points A(p = 5, = 70°, z =-3) and B(p = 2, 6 =-30°, z 1), find: (a) a unit vector in cartesian coordinates at A directed toward B; (b) a unit vector in cylindrical coordinates at A directed toward B; (c) a unit vector in cylindrical coordinates at B directed toward A.Given the following three vectors: A = -9î+7), B = -6î -10} and vector C has a magnitude of, |=9 and makes and angle of 0=297°. Determine: a) D = A - C + 3B and D b) The angle that vector D makes with respect to the positive "x" axis.
- Question 30 In a "left handed" plane polar coordinate system, the position P(r,0) is defined in terms of r and 0 where r is the magnitude of the position vector i and 0 is the angle between i and y- axis measured from'y-axis as seen in the figure. (a) Express the positon vector i in this "left handed" plane polar coordinates (LHPPC). (b) Show the f and ô unit vectors of this LHPPC. Show them in a graph such as the one given on the left. Also express them in terms of the unit vectors of Cartesian coordinates. dr (c) Calculate an expression velocity v = as a function dt of r and 0 in LHPPC. (d) Calculate the expression for acceleration a(r,0) in LHPPC.The x and y coordinates of point P are (-8.50 m, -7.00 m). What is the polar angle of point P?y 1 40 4N 65° 6N (d) What is the magnitude of the total force | A+B|? (e) What is the angle between the total force and the +x axis?
- Question VIIIProblem 3: Walking around Three players on a reality TV show are brought to the center of a large, flat field. Each is given a meter stick, a compass, a calculator, a shovel, and the following 3 displacements in order: A: 72.4 m, 32° east of north, B: 57.3 m, 36° south of west, C: 17.8 m due south. y (th) 17,8m C 32.0 57.3 m B 36.0 A 724 m The three displacements lead to the point in the field where the keys to a new Porsche are buried. Two of the players take the brown path, following the three displacements in order. However, the winner calculates the net displacement of all three vectors together (vector R) and follows the blue path, getting there faster than the other two contestents. For each calculation in the following questions, keep at least 2 decimal places for each value. (east)Two vectors A and B are shown in the figure. Vector A has a magnitude of r = 24.5 and an angle of 0A = 25.9°. Vector B has a magnitude of rB = 44.5 and an angle of 0B = 61.5°. The figure is not to scale. Express each vector in the figure using ijk unit vector notation, A = Axi + Ayj B = B₂i + B₂j where Ax, Ay, Bx, and By are the calculated values of the x- and y-components of vectors A and B, respectively. A = B = B TB OB TA 0
- Vector A = 4.5 i+ 3.2 j. Vector B = 4.5 i + 4.2 j. The dot product of the two %3D is C = A•B (i.e. A dot B). The value of C is:Vector A has a magnitude of 4 m and lies in the xy plane directed at 45 degrees counterclockwise from the positive x axis, whereas the vector B has a magnitude of 3m and lies in the yz plane directed at 30 degrees from the positive z axic. Find the cross product A x B and the angle between the vectors.Vectors A and B lie in the xy-plane. Vector À has a magnitude of 12.1 and is at an angle of 105.5° counterclockwise from the +x-axis. Vector B has a magnitude of 21.9 and is 250.3* from the +x-axis. Resolve A and B into components, and express using ijk unit vectors, A = Axi + Ayj + A-k B = B₂i + B₂j + B₂k where A., Ay, A₂ and B₁, B₁, and B₂ are the calculated values of the x-, y-, and z-components of vectors A and B, respectively. Ā = B = Find the magnitude and unit vector for the cross product between A and B. |ĀXB| = Identify the unit vector for AX B. j k