A) \[-\mathbf{i}+\mathbf{j}+\mathbf{k}\]
B) \[\mathbf{i}-\mathbf{j}+\mathbf{k}\]
C) \[\mathbf{i}+\mathbf{j}-\mathbf{k}\]
D) \[\mathbf{i}+\mathbf{j}+\mathbf{k}\]
Correct Answer: D
Solution :
Vector area \[=\frac{1}{2}(\overrightarrow{AB}\times \overrightarrow{AC})=\frac{1}{2}|(-\mathbf{i}+\mathbf{k})\times (-\mathbf{j}+\mathbf{k})|\] \[=\frac{1}{2}\left| \begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ -1 & 0 & 1 \\ 0 & -1 & 1 \\ \end{matrix} \right|=\frac{1}{2}(\mathbf{i}+\mathbf{j}+\mathbf{k})\] Hence by comparing, \[\overrightarrow{\alpha }=\mathbf{i}+\mathbf{j}+\mathbf{k}.\]You need to login to perform this action.
You will be redirected in
3 sec