Question 172: Motion in 2D & Vectors

Question

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

Accepted Answer

Let the two vectors are $$\overrightarrow A $$ and $$\overrightarrow B. $$
Given that, $$\left| {\overrightarrow A  + \overrightarrow B } ight| = \left| {\overrightarrow A  - \overrightarrow B } ight|$$
$$ 	herefore $$ $$\sqrt {{A^2} + {B^2} + 2AB\cos 	heta } $$ = $$\sqrt {{A^2} + {B^2} - 2AB\cos 	heta } $$
$$ \Rightarrow $$ $${4AB\cos 	heta }$$ = 0
$$ \because $$ $${4AB}$$ $$ 
e $$ 0
$$ 	herefore $$ $${\cos 	heta }$$ = 0
$$ \Rightarrow $$ $$	heta $$ = 90
o

Answer

45o

Answer

180o

Answer

0o

Answer

90o

Motion in 2D & Vectors

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

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