Question 50: Motion in 2D & Vectors

Question

Two vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ have equal magnitudes. If magnitude of $$\overrightarrow A $$ + $$\overrightarrow B $$ is equal to two times the magnitude of $$\overrightarrow A $$ $$-$$ $$\overrightarrow B $$, then the angle between $$\overrightarrow A $$ and $$\overrightarrow B $$ will be :

Accepted Answer

$$\sqrt {{A^2} + {A^2} + 2{A^2}\cos 	heta }  = 2\sqrt {{A^2} + {A^2} + 2{A^2}( - \cos 	heta )} $$
$$ \Rightarrow 2{A^2} + 2{A^2}\cos 	heta  = 8{A^2} + 8{A^2} - ( - \cos 	heta )$$
$$ \Rightarrow 5\cos 	heta  = 3$$
$$ \Rightarrow 	heta  = {\cos ^{ - 1}}\left( {{3 \over 5}} ight)$$

Answer

$${\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$

Answer

$${\sin ^{ - 1}}\left( {{1 \over 3}} \right)$$

Answer

$${\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$

Answer

$${\cos ^{ - 1}}\left( {{1 \over 3}} \right)$$

Motion in 2D & Vectors

Two vectors $\overrightarrow A and \overrightarrow B have equal magnitudes. If magnitude of \overrightarrow A + \overrightarrow B is equal to two times the magnitude of \overrightarrow A - \overrightarrow B , then the angle between \overrightarrow A and \overrightarrow B $ will be :

Choose the correct answer: