A) \[-17\hat{i}+21\hat{j}-97\hat{k}\]
B) \[17\hat{i}+21\hat{j}-123\hat{k}\]
C) \[-17\hat{i}-21\hat{j}+97\hat{k}\]
D) \[-17\hat{i}-21\hat{j}-97\hat{k}\]
Correct Answer: D
Solution :
We know that a vector perpendicular to \[\vec{a}\] and in the plane containing \[\vec{b}\] and \[\vec{c}\] is given by \[\vec{a}\times (\vec{b}\times \vec{c})\] Given \[\vec{a}=2\hat{i}+3\hat{j}-\hat{k},\] \[\vec{b}=\hat{i}+2\hat{j}-5\hat{k}\] and \[\vec{c}=3\hat{i}+5\hat{j}-\hat{k}\] \[\therefore \]\[\vec{b}\times \vec{c}=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 1 & 2 & -5 \\ 3 & 5 & -1 \\ \end{matrix} \right|=23\hat{i}-14\hat{j}-\hat{k}\] Now, \[\vec{a}\times (\vec{b}\times \vec{c})=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 2 & 3 & -1 \\ 23 & -14 & -1 \\ \end{matrix} \right|\] \[=(-3-14)\hat{i}-\hat{j}(-2+23)+\hat{k}(-28-69)\] \[=-17\hat{i}-21\hat{j}-97\hat{k}\] Which is the required vector.
You need to login to perform this action.
You will be redirected in
3 sec
