## Answer :

*Torque =*

**r x F****is the cross product of Force and distance between the force and the axis about which the torque is found.**

So

**is = ( - 5**

*torque**- 4*

**i***)*

**j***(4*

**x***- 10*

**i***)*

**j**= -5 * 4

*+ 5 * 10*

**i x i***- 4 * 4*

**i x j***+ 4 * 10*

**j x i**

**j x j**= 0 + 50

*16*

**k +***0*

**k +**= 66

*newton-m*

**k**the direction is in the +ve z axis and magnitude is 66 newton-metres

**Answer:**

66 N-m

**Explanation:**

**Torque as a function of displacement and Force is given by:-**

[tex]\tau = r \times F[/tex]

Displacement vector is given by, [tex]r = -5 \hat{i} -4\hat{j}[/tex]

Force vector is given by, [tex]F = 4 \hat{i} -10\hat{j} \ N[/tex]

**To find the torque:-**

[tex]\tou = \left[\begin{array}{ccc}i&-j&k\\-5&-4&0\\4&-10&0\end{array}\right][/tex]

**This solves to:-**

[tex]= [(-5\times-10)-(-4\times4)]\hat{k} \\ \\= [(50)-(-16)]\hat{k} \\ \\= 66 \ \hat{k}[/tex]

This means, a torque of 66 N-m will be applied in the positive z-axis.