Question 80: Motion in 2D & Vectors

Question

Two vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ have equal magnitudes. The magnitude  of $$\left( {\overrightarrow A  + \overrightarrow B } \right)$$ is 'n' times the magnitude of $$\left( {\overrightarrow A  - \overrightarrow B } \right)$$ . The angle between $${\overrightarrow A }$$ and $${\overrightarrow B }$$ is -

Accepted Answer

$$\left| {\overrightarrow A  + \overrightarrow B } ight| = 2a\cos 	heta /2$$      . . . (1)
$$\left| {\overrightarrow A  - \overrightarrow B } ight| = 2a\cos {{\left( {\pi  - 	heta } ight)} \over 2} = 2a\sin 	heta /2$$      . . . (2)
$$ \Rightarrow \,\,\,n\left( {2a\cos {	heta  \over 2}} ight) = 2a{{\sin 	heta } \over 2}$$
$$ \Rightarrow \,\,\,	an {	heta  \over 2} = n$$

Answer

$${\sin ^{ - 1}}\left[ {{{n - 1} \over {n + 1}}} \right]$$

Answer

$${\sin ^{ - 1}}\left[ {{{{n^2} - 1} \over {{n^2} + 1}}} \right]$$

Answer

$${\cos ^{ - 1}}\left[ {{{{n^2} - 1} \over {{n^2} + 1}}} \right]$$

Answer

$${\cos ^{ - 1}}\left[ {{{n - 1} \over {n + 1}}} \right]$$

Motion in 2D & Vectors

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