A) 3
B) 0
C) 1
D) 2
Correct Answer: A
Solution :
We have,\[\mathbf{\vec{u}}\cdot \mathbf{\hat{n}}=0\]and\[\mathbf{\vec{v}}\cdot \mathbf{\hat{n}}=0\] \[\Rightarrow \] \[\mathbf{\hat{n}}\bot \mathbf{\vec{u}}\]and\[\mathbf{\hat{n}}\bot \mathbf{\vec{v}}\] \[\Rightarrow \] \[\mathbf{\hat{n}}=\pm \frac{\mathbf{\vec{u}}\times \mathbf{\vec{v}}}{|\mathbf{\vec{u}}\times \mathbf{\vec{v}}|}\] Now, \[\mathbf{\vec{u}}\times \mathbf{\vec{v}}=(\widehat{\mathbf{i}}+\mathbf{\hat{j}})\times (\mathbf{\hat{i}}-\mathbf{\hat{j}})=-2\mathbf{\hat{k}}\] \[\mathbf{\hat{n}}=\pm \mathbf{\hat{k}}\] Hence,\[|\mathbf{\vec{w}}\cdot \mathbf{\vec{n}}|=(\mathbf{\hat{i}}+2\mathbf{\hat{j}}+3\mathbf{\hat{k}})\cdot (\pm \mathbf{\hat{k}})|\,\,=3\]You need to login to perform this action.
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