A) 1
B) \[-1\]
C) 0
D) none of these
Correct Answer: B
Solution :
Given, \[\vec{a}=\hat{i}+\hat{j}-\hat{k},\vec{b}=-\hat{i}+\hat{k}\]and \[\vec{c}=2\hat{i}+\hat{j}\] \[\because \] \[(\vec{a}+\lambda \vec{c})\bot \vec{b}\] \[\therefore \] \[(\vec{a}+\lambda \vec{c}).\vec{b}=0\] \[\Rightarrow \] \[[(\hat{i}+\hat{j}-\hat{k})+\lambda (2\hat{i}+\hat{j})].(-\hat{i}+\hat{k})=0\] \[\Rightarrow \] \[[(1+2\lambda )\hat{i}+(1+\lambda )\hat{j}-\hat{k}].(-\hat{i}+\hat{k})=0\] \[\Rightarrow \]\[(1+2\lambda )(-1)+(-1)=0\] \[\Rightarrow \] \[2\lambda =-2\] \[\Rightarrow \] \[\lambda =-1.\]
You need to login to perform this action.
You will be redirected in
3 sec
