Vectors Question 202
Question: The vectors from origin to the points A and B are $ \vec{A}=3\hat{i},-6\hat{j},+2\hat{k} $ and $ \vec{B}=2\hat{i}+,\hat{j},-2\hat{k} $ respectively. The area of the triangle OAB be
Options:
A) $ \frac{5}{2},\sqrt{17},sq,units $
B) $ \frac{2}{5},\sqrt{17},sq,unit $
C) $ \frac{3}{5},\sqrt{17},sq,unit $
D) $ \frac{5}{3},\sqrt{17},sq,unit $
Correct Answer: A [a] Given $ \overrightarrow{OA}=,\vec{a}=,3\hat{i}-6\hat{j}+2\hat{k} $ and
$ \overrightarrow{OB}=\vec{b}=,2\hat{i}+\hat{j}-2\hat{k} $ $ \ Therefore $ $ ,(\vec{a}\times \vec{b}),=,| ,\begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 3 & -6 & 2 \\ 2 & 1 & -2 \\ \end{matrix}, | $
$ =,(12-2),\hat{i}+(4+6)\hat{j}+,(3+12),\hat{k} $
$ =10\hat{i}+,10\hat{j}+15\hat{k} $ $ \Rightarrow $ $ |\vec{a}\times \vec{b}|=,\sqrt{10^{2}+,10^{2}+15^{2}} $
$ =,\sqrt{425}=,5\sqrt{17} $
Area of $ \Delta OAB=,\frac{1}{2}|\vec{a}\times ,\vec{b}|,=,\frac{5\sqrt{17}}{2},sq.\ unit $Show Answer
Answer:
Solution:
BETA
