Question # If the magnitudes of ( overrightarrow{mathrm{A}}, overrightarrow{mathrm{B}} ) and ( overrightarrow{mathrm{C}} ) are 12,5 and 13 units, respectively, and ( overrightarrow{mathrm{A}}+overrightarrow{mathrm{B}}=mathrm{C} ), then the angle between ( overrightarrow{mathrm{A}} ) and ( overrightarrow{mathrm{B}} ) is

# If the magnitudes of ( overrightarrow{mathrm{A}}, overrightarrow{mathrm{B}} ) and ( overrightarrow{mathrm{C}} ) are 12,5 and 13 units, respectively, and ( overrightarrow{mathrm{A}}+overrightarrow{mathrm{B}}=mathrm{C} ), then the angle between ( overrightarrow{mathrm{A}} ) and ( overrightarrow{mathrm{B}} ) is

(A) zero.

(B) ( pi )

(C) ( pi / 2 )

(D) ( pi / 4 )

Solution

( quad A+vec{B}=vec{c} )

( Rightarrow sqrt{A^{2}+B^{2}+2 A B cos theta=sqrt{c^{2}}} )

( Rightarrow A^{2}+B^{2}+2 A B cos theta=c^{2} )

( Rightarrow 12^{2}+5^{2}+2 times 12 times 5 cos theta=13^{2} )

( Rightarrow 169+120 cos theta=169 )

( Rightarrow cos 0=0 )

( Rightarrow theta=pi / 2 ) (c) Ans.