Q. If the re resultant of two vectors $overrightarrow{A}$ and $ overrightarrow{B} ,is, overrightarrow{C}$ and if the direction of $overrightarrow{ D}$ is reversed, and the resultant is , then

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If the re resultant of two vectors $overrightarrow{A}$ and $ overrightarrow{B} ,is, overrightarrow{C}$ and if the direction of $overrightarrow{ D}$ is reversed, and the resultant is , then

Solution:

$C^2 = A^2 + B^2 + 2AB , cos , theta , rightarrow (1)$

and $D^2 = A^2 + B^2 – 2AB , cos , theta , rightarrow (2)$

Adding equations (1) and (2)

$C^2 + D^2 = 2A^2 + 2B^2$

$ Rightarrow C^2 + D^2 = 2(A^2 + B^2)$