A) \[6\hat{i}-6\hat{j}+\frac{9}{2}\hat{k}\]
B) \[-3\hat{i}+3\hat{j}-9\hat{k}\]
C) \[-6\hat{i}+6\hat{j}-\frac{9}{2}\hat{k}\]
D) \[3\hat{i}-3\hat{j}+9\hat{k}\]
Correct Answer: A
Solution :
\[{{\vec{b}}_{1}}\,=\frac{(\vec{b}.\vec{a})\hat{a}}{1}\] \[=\left\{ \frac{(3\hat{j}+4\hat{k}).(\hat{i}+\hat{j})}{\sqrt{2}} \right\}\,\left( \frac{\hat{i}+\hat{j}}{\sqrt{2}} \right)\] \[=\frac{3(\hat{i}+\hat{j})}{\sqrt{2}\times \sqrt{2}}\,=\frac{3(\hat{i}+\hat{j})}{2}\] \[{{\vec{b}}_{1}}+{{\vec{b}}_{2}}=\vec{b}\] \[{{\vec{b}}_{2}}=\vec{b}-{{\vec{b}}_{1}}\] \[=\left( 3\hat{i}+4\hat{k} \right)\,-\frac{3}{2}\,(\hat{i}+\hat{j})\] \[\] \[{{b}_{1}}\times {{b}_{2}}\,=\left| \begin{matrix} i & j & k \\ \frac{3}{2} & \frac{3}{2} & 0 \\ -\frac{3}{2} & \frac{3}{2} & 4 \\ \end{matrix} \right|\]You need to login to perform this action.
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