A) \[\lambda =0\] only
B) \[\lambda =1\]
C) \[\lambda <1\]
D) \[\lambda >1\]
Correct Answer: D
Solution :
[d] Given. \[{{\vec{r}}_{1}}=\lambda \hat{i}+2\hat{j}+\hat{k}\] and \[{{\vec{r}}_{1}}=\hat{i}+(2-\lambda )\hat{j}+2\hat{k}\] \[\therefore \left| {{{\vec{r}}}_{1}} \right|>\left| {{{\vec{r}}}_{2}} \right|\] \[\Rightarrow \sqrt{{{\lambda }^{2}}+{{(2)}^{2}}+{{(1)}^{2}}}>\sqrt{{{(1)}^{2}}+{{(2-\lambda )}^{2}}+{{(2)}^{2}}}\] \[\Rightarrow \,\,\,\,\,{{\lambda }^{2}}+4+1>1+4+{{\lambda }^{2}}-4\lambda +4\] \[\Rightarrow \,\,\,\,5>9-4\lambda \] \[\Rightarrow \,\,\,\,4\lambda >4\] \[\Rightarrow \,\,\,\,\lambda >1\]
You need to login to perform this action.
You will be redirected in
3 sec
