Vector Algebra Question 174
Question: The moment about the point $ M(-2,,4,,-6) $ of the force represented in magnitude and position by $ \overrightarrow{AB} $ where the points A and B have the co-ordinates $ (1,,2,,-3) $ and $ (3,,-4,,2) $ respectively, is
[MP PET 2000]
Options:
A) 8i - 9j - 14k
B) 2i - 6j + 5k
C) - 3i + 2j - 3k
D) - 5i + 8j - 8k
Show Answer
Answer:
Correct Answer: A
Solution:
- Force $ \mathbf{F}=\overrightarrow{AB}=( 3-1 ),i+( -4-2 ),j+( 2+3 ),k $
$ =2i-6j+5k $
Moment of Force $ \overrightarrow{F} $ w.r.t $ M=\overrightarrow{MA}\times \overrightarrow{F} $
$ \because ,\overrightarrow{MA}=( 1+2 ),i+( 2-4 ),j+( -3+6 ),k $ $ =3i-2j+3k $
Now $ \overrightarrow{MA}\times \overrightarrow{F}=| ,\begin{matrix} i & j & k \\ 3 & -2 & 3 \\ 2 & -6 & 5 \\ \end{matrix}, | $ $ =\mathbf{i},( -10+18 )+\mathbf{j},( 6-15 )+\mathbf{k},( -18+4 ) $ $ =8\mathbf{i}-9\mathbf{j}-14\mathbf{k} $ .
BETA
