Angular momentum and torque of a particle

[physics_geek]

Homework Statement

A particle is located at the vector position =(4.00i + 5.00j) m and a force exerted on it is given by =(2.00i + 1.00j) N.
a. What is the torque acting on the particle about the origin?
b. Consider another point about which the torque caused by this force on this particle will be in the opposite direction and half as large in magnitude. Select the following conditions that are true.
No such point can exist.
Only one such point can exist.
Multiple such points can exist.
No such a point can lie on the y-axis.
Only one such point can lie on the y-axis.
Multiple such points can lie on the y-axis.

c. Determine the position vector of such a point.

Homework Equations

cross products A x B

The Attempt at a Solution

so i got part a..its -6k
i need help with parts b and c please

 

[jeffreydk]

First, you know that a force in the opposite direction and half the magnitude is just $3\hat{k}$. So take a look at the torque;

$$\tau=\mathbf{r}\times\mathbf{F}=\begin{vmatrix}<br /> \hat{i} & \hat{j} & \hat{k} \\<br /> a & b & 0 \\<br /> 2 & 1 & 0 <br /> \end{vmatrix}<br /> =[a-2b]\hat{k}$$

So what possiblities could you have here for $a$ and $b$ (which are of course the position components) if you know the torque must be equal to $3\hat{k}$?