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

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

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

Column $-I$	Column $-II$
$(a)$ $\vec A \,.\,\,\vec B \, = \,\,0$	$(i)$ $\theta = \,{0^o}$
$(b)$ $\vec A \,.\,\,\vec B \, = \,\,+8$	$(ii)$ $\theta = \,{90^o}$
$(c)$ $\vec A \,.\,\,\vec B \, = \,\,4$	$(iii)$ $\theta = \,{180^o}$
$(d)$ $\vec A \,.\,\,\vec B \, = \,\,-8$	$(iv)$ $\theta = \,{60^o}$

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

Similar Questions

If a vector $\vec A$ is parallel to another vector $\vec B$ then the resultant of the vector $\vec A \times \vec B$ will be equal to

Show that the area of the triangle contained between the vectors $a$ and $b$ is one half of the magnitude of $a \times b .$

If $\overrightarrow {\rm A} = 2\hat i + 3\hat j - \hat k$ and $\overrightarrow B = - \hat i + 3\hat j + 4\hat k$ a unit vector perpendicular to both $\overrightarrow A $ and $\overrightarrow B $ will be

If $A$ is a unit vector in a given direction, then the value of $\hat{ A } \cdot \frac{d \hat{ A }}{d t}$ is