vec A, = ,(hat i, + ,hat j) અને vec B, = ,(2h | 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

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

કોલમ $-I$	કોલમ $-II$
$(a)$ $\left\| {\vec A \, \times \,\,\vec B } \right\|\, = \,\,0$	$(i)$ $\theta = \,{30^o}$
$(b)$ $\left\| {\vec A \, \times \,\,\vec B } \right\|\, = \,\,8$	$(ii)$ $\theta = \,{45^o}$
$(c)$ $\left\| {\vec A \, \times \,\,\vec B } \right\|\, = \,\,4$	$(iii)$ $\theta = \,{90^o}$
$(d)$ $\left\| {\vec A \, \times \,\,\vec B } \right\|\, = \,\,4\sqrt 2$	$(iv)$ $\theta = \,{0^o}$

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