The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{R_1}$. If vector $\vec{B}$ is reversed,the resultant becomes $\vec{R_2}$. What is the value of $R_1^2 + R_2^2$?

Two vectors of magnitude $3$ and $4$ have a resultant which makes angles $\alpha$ and $\beta$ respectively with them (given $\alpha + \beta \neq 90^o$).

The magnitudes of vectors $\overrightarrow{A}$,$\overrightarrow{B}$,and $\overrightarrow{C}$ are $12$,$5$,and $13$ units respectively,and $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$. Then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

Explain the parallelogram method for vector addition. Also,explain how this is comparable to the triangle method.

Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $n$ times the magnitude of $(\vec A - \vec B)$. The angle between $\vec A$ and $\vec B$ is

$A$ unit vector in the direction of the resultant vector of $\vec{A} = -2 \hat{i} + 3 \hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + 2 \hat{j} - 4 \hat{k}$ is