Question # If ( overrightarrow{mathrm{A}} cdot overrightarrow{mathrm{B}}=|overrightarrow{mathrm{A}} times overrightarrow{mathrm{B}}|, ) angle between ( overrightarrow{mathrm{A}} ) and ( overrightarrow{mathrm{B}} ) is

# If ( overrightarrow{mathrm{A}} cdot overrightarrow{mathrm{B}}=|overrightarrow{mathrm{A}} times overrightarrow{mathrm{B}}|, ) angle between ( overrightarrow{mathrm{A}} ) and ( overrightarrow{mathrm{B}} ) is

(a) ( 180^{circ} )

(b) ( 90^{circ} )

( (c) 0^{circ} )

( (d) 45^{circ} )

Solution

( vec{A} . vec{B}=|vec{A}||B| cdot cos theta )

( vec{A} times vec{B}=|vec{A}| cdot|vec{B}| cdot sin theta mid )

( So_{} vec{A} cdot vec{B}=|vec{A} times vec{B}| )

( begin{aligned} A|A||B| cos theta=|A||B| &=sin theta cos theta &=sin{theta} therefore quad theta &=45 end{aligned} )