Let vec A, = ,(hat i, + ,hat j), a | vedclass

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Question

$\begin{array}{l}
If\,\vec C = a\hat i + b\hat j\,then\,\vec A.\vec C = \vec A.\vec B\
a + b = 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\

Vedclass · Accepted Answer

$\sqrt {\frac{5}{9}} $

Vedclass · Answer

$\begin{array}{l}
If\,\vec C = a\hat i + b\hat j\,then\,\vec A.\vec C = \vec A.\vec B\
a + b = 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i ight)\
\vec B.\vec C = \vec A.\vec B\
2a - b = 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} ight)\
Solving\,equation\,\left( i ight)\,and\,\left( {ii} ight)\,\,we\,get\
a = \frac{1}{3},\,b = \frac{2}{3}\
Magnitude\,of\,coplanar\,vector,\
\left| {\vec C} ight| = \sqrt {\frac{1}{9} + \frac{4}{9}}  = \sqrt {\frac{5}{9}} 
\end{array}$

Let $\vec A\, = \,(\hat i\, + \,\hat j)\,$ and $\vec B\, = \,(2\hat i\, - \,\hat j)\,.$ The magnitude of a coplanar vector $\vec C$ such that $\vec A\cdot \vec C\, = \,\vec B\cdot \vec C\, = \vec A\cdot \vec B$ is given by

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