A) \[\frac{2}{3}\]
B) \[\frac{3}{2}\]
C) 2
D) 3
Correct Answer: B
Solution :
\[\mathbf{a}\times \mathbf{b}=\left| \,\begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 2 & 1 & -2 \\ 1 & 1 & 0 \\ \end{matrix}\, \right|=2\mathbf{i}-2\mathbf{j}+\mathbf{k}\] \[\therefore \,\,\,|\mathbf{a}\times \mathbf{b}|\,=\sqrt{4+4+1}=3\] \[|\mathbf{c}-\mathbf{a}|=2\sqrt{2}\Rightarrow \,|\mathbf{c}-\mathbf{a}{{|}^{2}}={{(\mathbf{c}-\mathbf{a})}^{2}}=8\] \[\Rightarrow \,|\mathbf{c}{{|}^{2}}-2\mathbf{a}.\mathbf{c}+|\mathbf{a}{{|}^{2}}=8\Rightarrow \,|\mathbf{c}{{|}^{2}}-2|\mathbf{c}|+9=8\] \[\Rightarrow \,|\mathbf{c}{{|}^{2}}-2|\mathbf{c}|+1=0\Rightarrow \,|\mathbf{c}|=1\] \[\therefore \,\,\,|(\mathbf{a}\times \mathbf{b})\times \mathbf{c}|\,=\,|\mathbf{a}\times \mathbf{b}|\,|\mathbf{c}|\sin 30{}^\circ =\frac{3}{2}\].
You need to login to perform this action.
You will be redirected in
3 sec
