Question 177: 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

45
o

Answer

180
o

Answer

0
o

Answer

90
o

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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