Vector Algebra Question 58
Question: A force $ \vec{F}=3\hat{i}+4\hat{j}-3\hat{k} $ is applied at the point P, whose position vector is $ \overrightarrow{r}=\widehat{2i}-2\hat{j}-3\hat{k} $ . What is the magnitude of the moment of the force about the origin?
Options:
A) 23 units
B) 19 units
C) 18 units
D) 21 units
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] Moment of force, $ m=\overset{\to }{\mathop{r}},\times \overset{\to }{\mathop{F}}, $
$ m= \begin{vmatrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 2 & -2 & -3 \\ 3 & 4 & -3 \\ \end{vmatrix} $
$ =\hat{i}(6+12)-\hat{j}(-6+9)+\hat{k}(8+6) $ $ =18\hat{i}-3\hat{j}+14\hat{k} $
$ =\sqrt{{{(18)}^{2}}+{{(-3)}^{2}}+{{(14)}^{2}}} $
$ =\sqrt{529}=23 $ units.
BETA
