A) 25
B) 50
C) 144
D) None of these
Correct Answer: B
Solution :
[b] Let \[{{\vec{r}}_{1}}=a\hat{i}+b\hat{j}+c\hat{k},{{\vec{r}}_{2}}=3\hat{i}+4\hat{j}+5\hat{k}\] \[|{{\vec{r}}_{1}}\times {{\vec{r}}_{2}}{{|}^{2}}\le |{{\vec{r}}_{1}}{{|}^{2}}|{{\vec{r}}_{2}}{{|}^{2}}...(1)\] Now, \[{{\vec{r}}_{1}}\times {{\vec{r}}_{2}}=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ a & b & c \\ 3 & 4 & 5 \\ \end{matrix} \right|\] \[=\hat{i}(5b-4c)+\hat{j}(3c-5a)+\hat{k}(4a-3b)\] So, from (1): \[{{(5b-4c)}^{2}}+{{(3c-5a)}^{2}}+{{(4a-3b)}^{2}}\le 50\]
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