Embibe Experts Solutions for Exercise 1: EXERCISE 11.1

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are position vectors of $A$ and $B$ respectively, then the position vector of a point $C$ in $AB$ produced such that $\overrightarrow{AC}=3\overrightarrow{AB}$ is

If $G$ and $G^{\text{'}}$ are the centroids of the triangles $A B C$ and $A^{\text{'}} B^{\text{'}} C^{\text{'}},$ then $\overrightarrow{AA\text{'}}+\overrightarrow{BB\text{'}}+\overrightarrow{CC\text{'}}$ is equal to

Let $ABCDEF$ be a regular hexagon. If $\overrightarrow{AD}=x\overrightarrow{BC}$ and $\overrightarrow{CF}=y\overrightarrow{AB},$ then $xy=$

$\overrightarrow{AB}=3\hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{AC}=\hat{i}-\hat{j}+3\hat{k}.$ If the point $P$ on the line segment $BC$ is equidistant from $AB$ and $AC,$ then $\overrightarrow{AP}$ is

If the vectors $\overrightarrow{AB}=3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a triangle $ABC,$ then the length of the median through $A$ is

$A,B,C,D$ and $E$ are five coplanar points, then $\overrightarrow{DA}+\overrightarrow{DB}+\overrightarrow{DC}+\overrightarrow{AE}+\overrightarrow{BE}+\overrightarrow{CE}$ is equal to

The vectors $\hat{i}+\hat{j}, \hat{j}+\hat{k}$ and $\hat{k}+\hat{i}$ are

Let $\alpha , \beta$ and $\gamma$ be the distinct real numbers. The points with position vectors $\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}, \beta \hat{i}+\gamma \hat{j}+\alpha \hat{k}$  and $\gamma \hat{i}+\alpha \hat{j}+\beta \hat{k}$ forms