Find the magnitude of the force

[munther]

A wrench 30cm long lies along the positive y-axis and grips a bolt in the origin. A force is applied in the
direction < 0; 3; -4 > at the end of the wrench. Find the magnitude of the force needed to supply 100J of
torque to the bolt.

how can i solve it?

r=<0,.3,0>
F=<0,3,4>
T= r X F =100
then i solved it by finding the det = 100

|i j k|
|0 .3 0| = 100
|0 3x -4x|

then x = 83.333 N

but the answer is wrong Why?

 

[malawi_glenn]

you get x = 83.333

but the magniture of the force is sqrt((3x)^2 + (-4x)^2 ) = 416.7 N

magnitude of vector v=(a,b,c) is sqrt(aa + bb+ cc)