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

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Vedclass · Accepted Answer

$0$

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 ....... $^o$

Similar Questions

The vectors $\vec{A}$ and $\vec{B}$ are such that

$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$

The angle between the two vectors is

Magnitude of vector which comes on addition of two vectors, $6\hat i + 7\hat j$ and $3\hat i + 4\hat j$ is

Match List$- I$ with List$- II.$

$[Image]$

Choose the correct answer from the options given below :

Three concurrent forces of the same magnitude are in equilibrium. What is the angle between the forces Also name the triangle formed by the forces as sides

What vector must be added to the two vectors $\hat i - 2\hat j + 2\hat k$ and $2\hat i + \hat j - \hat k,$ so that the resultant may be a unit vector along $X-$axis