2. Solved Papers
  3. Manipal Engineering

Manipal Engineering Manipal Engineering Solved Paper-2010

  • question_answer
    Let\[\overrightarrow{\mathbf{u}}=\widehat{\mathbf{i}}+\widehat{\mathbf{j}}\],\[\overrightarrow{\mathbf{v}}=\widehat{\mathbf{i}}-\widehat{\mathbf{j}}\]and\[\overset{\to }{\mathop{\mathbf{w}}}\,=\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}+3\widehat{\mathbf{k}}\], if\[\widehat{\mathbf{n}}\]is a unit vector such that\[\mathbf{\vec{u}}\cdot \widehat{\mathbf{n}}=0\]and \[\overrightarrow{\mathbf{v}}\cdot \widehat{\mathbf{n}}=0\], then\[|\overset{\to }{\mathop{\mathbf{w}}}\,.\widehat{\mathbf{n}}|\]is equal to

    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.
You will be redirected in 3 sec spinner