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A wrench 1m long lies along the positive y-axis and grips a bolt at the origin (i.e. the wrench can be represented by vector <0,1,0>). A force is applied in the direction of the unit vector <0, 1/sqrt(2), 1/sqrt(2)> at the end of the wrench. Find the magnitude of the force in Newtons (N) needed to supply 5sqrt(2) N*m of torque to the bolt.  torque = | r x F |  if r = <0,1,0> and F = <0, 1/sqrt(2), 1/sqrt(2)> so the torque is equal to the magnitude of the cross product of these two vectors but I don't understand how to get incorporate the 5sqrt(2) N*m I know that the magnitude of the cross product must be equal to 5sqrt(2) but I am not sure how to work backwards to that answer, please help!.

A wrench 1m long lies along the positive y-axis and grips a bolt at the origin (i.e. the wrench can be represented by vector <0,1,0>). A force is applied in the direction of the unit vector <0, 1/sqrt(2), 1/sqrt(2)> at the end of the wrench. Find the magnitude of the force in Newtons (N) needed to supply 5sqrt(2) N*m of torque to the bolt.  torque = | r x F |  if r = <0,1,0> and F = <0, 1/sqrt(2), 1/sqrt(2)> so the torque is equal to the magnitude of the cross product of these two vectors but I don't understand how to get incorporate the 5sqrt(2) N*m I know that the magnitude of the cross product must be equal to 5sqrt(2) but I am not sure how to work backwards to that answer, please help!.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 31E
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A wrench 1m long lies along the positive y-axis and grips a bolt at the origin (i.e. the wrench can be represented by vector <0,1,0>). A force is applied in the direction of the unit vector <0, 1/sqrt(2), 1/sqrt(2)> at the end of the wrench. Find the magnitude of the force in Newtons (N) needed to supply 5sqrt(2) N*m of torque to the bolt. 

torque = | r x F | 

if r = <0,1,0> and F = <0, 1/sqrt(2), 1/sqrt(2)> so the torque is equal to the magnitude of the cross product of these two vectors but I don't understand how to get incorporate the 5sqrt(2) N*m I know that the magnitude of the cross product must be equal to 5sqrt(2) but I am not sure how to work backwards to that answer, please help!.

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