As noted in the text, the scalar product between two vectors A and B can becalculated using trigonometry as:Ả B = \Ä||B| cos 0and the vector product as:ẢxB = |Ã||B| sin 0 fAIn words, the scalar product between vectors A and B is the product of theirmagnitudes and the cosine of the angle between them. The vector productbetween vectors A and B is the product of their magnitudes and the sine of theangle between them. The direction of the resulting vector is perpendicular tothe plane containing the vectors, with the sign of the vector following the right-hand rule.The right-hand rule is as follows: begin at vector A and curl the fingers of yourright hand toward vector B. The direction of your thumb is the direction of theresulting vector. In the traditional sense, the positive direction is above ahorizontal plane and the negative direction is below it.These quantities can also be calculated if the vectors are expressed in (i,j,k)notation. IfA = Ayî + Ayƒ + A,kandB = B,1 + B,} + B,kthenÃ·B = A,B, + A,By + A,B,andAxB = \A Ay Az =(A,B, - A,B2)î + (A,B, – A,Bx)} + (A, B,- Ay Bx)k|Bx By Bz53% Both the scalar and vector product have applications in mechanics. Thedisplacement vector and force vector can be multiplied by both methods,resulting in different physical quantities.If multiplied as a scalar product, the resulting quantity is the work done whilepushing or pulling an object from one location to another:W = d = Fd cos 0If multiplied as a scalar product, the result is the torque acting on the object,causing it to begin spinning about an axis, or change its rate of spin:T= ixF = Fr sin 0 înWhen considering work done, the displacement is usually symbolized with a d'(as in scalar distance) whereas with torque, the displacement is usuallysymbolized with an 'r' (as in the radius of a spinning circle).In this challenge exercise, we are asking you to confirm that both methods ofcalculating the scalar and vector products.Let a displacement vector in the (X,Y) plane be 5.0 m at a 30 degree angle withrespect to the x-axis and the force vector 6.0 N at a -45 degree angle withrespect to the x-axis.Calculate the work done by the force in moving an object that distance usingboth methods (trigonometry and vector components).Then calculate the torque acting at that displacement by that force about theorigin of the axis system, including the direction of the torque. (Hint: it will beeither the +Z or -Z direction.)Your solutions should show all the steps necessary to determine the finalanswers.53%

Given , displacement vector is 5m at a 30 degree with respect to x axis. force vector is…

Let a displacement vector in the (X,Y) plane be 5.0 m at a 30 degree angle with respect to the x-axis and the force vector 6.0 N at a -45 degree angle with respect to the x-axis. Calculate the work done by the force in moving an object that distance using both methods (trigonometry and vector components). Then calculate the torque acting at that displacement by that force about the origin of the axis system, including the direction of the torque. (Hint: it will be

Let a displacement vector in the (X,Y) plane be 5.0 m at a 30 degree angle with respect to the x-axis and the force vector 6.0 N at a -45 degree angle with respect to the x-axis. Calculate the work done by the force in moving an object that distance using both methods (trigonometry and vector components). Then calculate the torque acting at that displacement by that force about the origin of the axis system, including the direction of the torque. (Hint: it will be

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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