A force F  = 4i – 5j  + 3k  is acting a point (r_1 )  = i  + 2j  + 3k . The torque acting about a point (r_2 )  = 3i  – 2j  – 3k  is

Q: A force $\vec{F}  = 4\hat{i} – 5 \hat{j}  + 3 \hat{k}  $ is acting a point $ \vec{r_1}   = \hat{i}  + 2 \hat{j}  + 3 \hat{k} $ . The torque acting about a point $ \vec{r_2 }  = 3 \hat{i}  – 2 \hat{j}  – 3 \hat{k}  $ is

(a) zero

(b) $ 42 \hat{i}  – 30 \hat{j}  + 6 \hat{k} $

(c) $ 42 \hat{i}  + 30 \hat{j}  + 6 \hat{k} $

(d) $ 42 \hat{i} + 30 \hat{j}  – 6 \hat{k} $

Click to See Answer :
Ans: (d)
Sol: $\displaystyle Torque \; \vec{\tau} = \vec{r} \times \vec{F} $

$\displaystyle \vec{r} = \vec{r_1} – \vec{r_2} $

$\displaystyle \vec{r} = (\hat{i}  + 2 \hat{j}  + 3 \hat{k} ) – (3 \hat{i}  – 2 \hat{j}  – 3 \hat{k}) $

$\displaystyle \vec{r} = (- 2\hat{i}  + 4 \hat{j}  + 6 \hat{k} ) $

$\displaystyle \vec{\tau} = (- 2\hat{i}  + 4 \hat{j}  + 6 \hat{k} ) \times (4\hat{i} – 5 \hat{j}  + 3 \hat{k} ) $