Question 194: Motion in 2D & Vectors

Question

The vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ are such  that $$\left| {\overrightarrow A  + \overrightarrow B } \right| = \left| {\overrightarrow A  - \overrightarrow B } \right|.$$ The angle between the  two vectors is

Accepted Answer

$${\left| {\overrightarrow A  + \overrightarrow B } ight|^2} = {\left| {\overrightarrow A  - \overrightarrow B } ight|^2}$$
$$ = {\left| {\overrightarrow A } ight|^2} + {\left| {\overrightarrow B } ight|^2} + 2\overrightarrow A \overrightarrow B  = {A^2} + {B^2} + 2AB\cos 	heta $$
$$ = {\left| {\overrightarrow A  - \overrightarrow B } ight|^2} = {\left| {\overrightarrow A } ight|^2} + {\left| {\overrightarrow B } ight|^2} - 2\overrightarrow A .\overrightarrow B $$
$$ = {A^2} + {B^2} - 2AB\cos 	heta $$
So, A
2
+ B
2
+ 2AB cos $$	heta $$
= A
2
+ B
2
Ã¢ÂÂ 2AB cos $$	heta $$
4AB cos$$	heta $$ = 0 $$ \Rightarrow $$ cos$$	heta $$ = 0
$$	heta $$ = 90ÃÂº
So, angle between A & B is 90ÃÂº.

Answer

45o

Answer

90o

Answer

60o

Answer

75o

Motion in 2D & Vectors

The vectors $\overrightarrow A and \overrightarrow B are such that \left| {\overrightarrow A + \overrightarrow B } \right| = \left| {\overrightarrow A - \overrightarrow B } \right|.$ The angle between the two vectors is

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