Addition of Vectors

Given that $\overrightarrow{P}+\overrightarrow{Q}+\overrightarrow{R}=\overrightarrow{0}.$ Two out of the three vectors are equal in magnitude. The magnitude of the third vector is $\sqrt{2}$ times that of the other two. Which of the following can be the angles between these vectors?

Three forces starts acting simultaneously on a particle moving with velocity $\overrightarrow{v}.$ These forces are represented in magnitude and direction by the three sides of a triangle $ABC$ (as shown). The particle will now move with velocity

$\overrightarrow{a}=(3,5,7)\text{ and }\overrightarrow{b}=(2,4,6)$ are vectors in Cartesian form. Find $\overrightarrow{a}+\overrightarrow{b}$.

$\overrightarrow{b}=(2,3,5)\text{ and }\overrightarrow{a}=(2,1,3)$ are vectors in Cartesian form. Find $\overrightarrow{a}+\overrightarrow{b}$.

$\overrightarrow{b}=(1,2,3)\text{ and }\overrightarrow{a}=(2,4,6)$ are vectors in Cartesian form. Find $\overrightarrow{a}+\overrightarrow{b}$.

If $\overrightarrow{OB}=3\hat{i}+2\hat{j}+5\hat{k} \& \overrightarrow{OA}=4\hat{i}+5\hat{j}+2\hat{k}$, then find $\overrightarrow{AB}$.

If $\overrightarrow{OB}=2\hat{i}+3\hat{j}+4\hat{k} \& \overrightarrow{OA}=4\hat{i}+5\hat{j}+2\hat{k}$, then find $\overrightarrow{AB}$.

If $\overrightarrow{OB}=\hat{i}+3\hat{j}+2\hat{k} \& \overrightarrow{OA}=2\hat{i}+\hat{j}+4\hat{k}$, then find $\overrightarrow{AB}$.

If $\overrightarrow{OB}=\hat{i}+3\hat{j}+2\hat{k} \& \overrightarrow{OA}=3\hat{i}+2\hat{j}+2\hat{k}$, then find $\overrightarrow{AB}$.

If $\overrightarrow{a}=\hat{i}+2\hat{j}+4\hat{k}$ and $\overrightarrow{b}=4\hat{i}+2\hat{j}+6\hat{k}$, then verify associative property of vector addition.

If $\overrightarrow{a}=\hat{i}+2\hat{j}+3\hat{k}$ and $\overrightarrow{b}=4\hat{i}+2\hat{j}+6\hat{k}$, then verify associative property of vector addition.

If $\overrightarrow{a}=\hat{i}+2\hat{j}+3\hat{k}$$\text{ and }\overrightarrow{b}=3\hat{i}+2\hat{j}+2\hat{k}$, then verify associative property of vector addition.

If $\overrightarrow{a}=3\hat{i}+2\hat{j}+\hat{k}$$\text{ and }\overrightarrow{b}=3\hat{i}+2\hat{j}+2\hat{k}$, then verify associative property of vector addition.

$\overrightarrow{a}=\hat{i}+2\hat{j}+4\hat{k}$. Find the sum of given vector with additive identity of vectors.

$\overrightarrow{a}=4\hat{i}+2\hat{j}+6\hat{k}$. Find the sum of given vector with additive identity of vectors.

$\overrightarrow{a}=\hat{i}+2\hat{j}+3\hat{k}$. Find the sum of given vector with additive identity of vectors.

$\overrightarrow{a}=3\hat{i}+2\hat{j}+\hat{k}$. Find the sum of given vector with additive identity of vectors.

$\overrightarrow{a}=\left(3,5,7\right)$ and $\overrightarrow{b}=\left(2,4,6\right)$ are vectors in Cartesian form. Find $\overrightarrow{a}-\overrightarrow{b}$.

$\overrightarrow{b}=\left(3,5,1\right)$ and $\overrightarrow{a}=\left(1,6,2\right)$ are vectors in Cartesian form. Find $\overrightarrow{a}-\overrightarrow{b}$.