What is the relationship between the torque and position vectors?

[nameVoid]

A 5.0 kg object at r= i^+2j^+3k^ meters has an acceleration a=5i^+6j^-7k^ m/s^2

a)what is the objects torque around the origin of the cordinate system
b)prove that the torque is perpendicular to the position vector r

a)
t^=rXma=-10<16,-11,2>
t=-10(381)^1/2

b)
<1,2,3>*<16,-11,2>=0

 

[Mark44]

Do you have a question? What you have looks fine to me.

 

[nameVoid]

I was marked wrong for that on an exam

 

[Mark44]

The torque T is a vector, and I get what you get.

The magnitude of the torque (which wasn't asked for), |T| is +10*sqrt(381), not -10sqrt(381) as you had.

The dot product of <1, 2, 3> and 10<-16, 11, -2> is 0, so the two vectors are perpendicular. Maybe you were supposed to prove that the torque and position vectors are perpendicular in general, not just for the values in this problem.