If | A + B |=| A |+| B | the angle between ov | vedclass

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Question

For two vectors $A \square A ightarrow$ and $B \square B ightarrow$, the angle between them being $	heta 	heta$, the magnitude of the resultant

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Vedclass · Answer

For two vectors $A \square A ightarrow$ and $B \square B ightarrow$, the angle between them being $	heta 	heta$, the magnitude of the resultant vector $A + B ightarrow A + B ightarrow$ is given by,

$| A + B |=\sqrt{| A |^2+| B |^2+2 AB \cos 	heta}$

Now in the problem we've,

$| A + B |=| A |+| B |$

Squaring on both sides,

$\begin{array}{l}| A + B |^2=(| A |+| B |)^2 \| A |^2+| B |^2+2| A || B | \cos 	heta=| A |^2+| B |^2+2| A || B | \\Rightarrow \cos 	heta=1\end{array}$

assuming neither of the vectors are $zero$ vectors.

If $| A + B |=| A |+| B |$ the angle between $\overrightarrow A $and $\overrightarrow B $ is ....... $^o$

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