Addition of Vectors

Let $OACB$ be parallelogram with $O$ at origin & $OC$ a diagonal. Let $D$ be the mid point of $OA$. Then the ratio in which $OC$ intersect $BD$ is

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?

If $\overrightarrow{P}+\overrightarrow{Q}=\overrightarrow{R}, \left|\overrightarrow{P}\right|=\left|\overrightarrow{Q}\right|=\left|\overrightarrow{R}\right|$, then angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$ is

The position vectors of the vertices $\mathrm{P}, \mathrm{Q} \mathrm{and} \mathrm{R}$ of $∆\mathrm{PQR}$ are $-\hat{i}+2\hat{j}+4\hat{k}, 3\hat{i}+6\hat{j}+8\hat{k} \mathrm{and} 4\hat{i}+\hat{j}+\hat{k}$ respectively.

Which of the following is the vector that represents the median $\overrightarrow{\mathrm{PS}}$?

If $A=3\hat{i}-4\hat{j}$ and $B=-\hat{i}-4\hat{j}$, then calculate $\overrightarrow{A}+\overrightarrow{B}$ and $\left|\overrightarrow{A}+\overrightarrow{B}\right|$.

Consider the two vector $\overrightarrow{A}$ and $\overrightarrow{B}$, the magnitude of their sum i.e $\left|\overrightarrow{A}+\overrightarrow{B}\right|$

In quadrilateral $ABCD, \overrightarrow{AB}=\overrightarrow{a}, \overrightarrow{BC}=\overrightarrow{b}, \overrightarrow{DA}=\overrightarrow{a}-\overrightarrow{b}, M$ is the midpoint of $BC$ and $X$ is a point on $DM$ such that $\overrightarrow{DX}=\frac{4}{5}\overrightarrow{DM}$. Then the points $A, X$ and $C$

If $\overrightarrow{a}=2\hat{ı}+3\hat{ȷ}-4\hat{k}$ and $\overrightarrow{b}=\hat{ı}+3\hat{ȷ}+2\hat{k}$, then a unit vector in the direction of $\overrightarrow{a}+\overrightarrow{b}$ is

If $\overrightarrow{A},\overrightarrow{B }\& \overrightarrow{C}$ represent unit vectors in each case, then which vector combination(s) results in a unit vector$?$

If $\overrightarrow{A},\overrightarrow{B }\& \overrightarrow{C}$ represent unit vectors in each case, then which vector combination(s) results in a unit vector$?$

Unit vectors along the diagonals of the parallelogram whose adjacent sides are $\hat{i}+\hat{j}+\hat{k} \& \hat{i}-\hat{j}+\hat{k}$, are

Let $\overrightarrow{a}=\hat{i}+\hat{j}-\hat{k}, \overrightarrow{b}=5\hat{i}-3\hat{j}-3\hat{k}, \overrightarrow{c}=3\hat{i}-\hat{j}-2\hat{k}.$ If collinear with $\overrightarrow{c}$ and $\left|\overrightarrow{r}\right|=\left|\overrightarrow{a}+\overrightarrow{b}\right|.$ Then $\overrightarrow{r}$ equals

If the vector $4\hat{\mathrm{i}}-7\hat{\mathrm{j}}-2\hat{\mathrm{k}}$,$\hat{\mathrm{i}}+5\hat{\mathrm{j}}-3\hat{\mathrm{k}}$ and $3\hat{\mathrm{i}}-\lambda \hat{\mathrm{j}}+\hat{\mathrm{k}}$ form a triangle then $\lambda$ =

The figure shows a parallelogram $\mathrm{ABCD}$. Then which of the following option is correct?

If $O$ is the circumcentre and $O^{\text{'}}$ is the orthocentre of a triangle $ABC$ and if $\overrightarrow{AP}$ is the circumdiameter then $\overrightarrow{A{O}^{\text{'}}}+\overrightarrow{O^{\text{'}}B}+\overrightarrow{O^{\text{'}}C}=$

$E$ and $F$ are the midpoints of $AC$ and $BD$ of the quadrilateral $ABCD$respectively. Then the value of $\overrightarrow{AB}+\overrightarrow{AD}+\overrightarrow{CB}+\overrightarrow{CD}=$_____.

The two adjacent sides of parallelogram are $2\hat{i}-4\hat{j}+5\hat{k}$ and $\hat{i}-2\hat{j}-3\hat{k}$. The unit vector parallel to its diagonal which starts at the common vertex of the above two sides, is

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three vectors such that $\left|\overrightarrow{a}\right|=\left|\overrightarrow{b}\right|=2,\overrightarrow{a}·\overrightarrow{b}=2$ and $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0$, then $\left|\overrightarrow{c}\right|$ is equal to

If $ABCDEF$ is a regular hexagon with $\overrightarrow{AB}=\overrightarrow{a}$ and $\overrightarrow{BC}=\overrightarrow{b}$ then $\overrightarrow{CE}$ equals