Embibe Experts Solutions for Chapter: Vector Algebra, Exercise 1: Exercise

Show that three points $A(-2\hat{i}+3\hat{j}+5\hat{k}), B(\hat{i}+2\hat{j}+3\hat{k}) \mathrm{and} C(7\hat{i}-\hat{k})$ are collinear.

If the sum of two unit vectors is a unit vector, show that the magnitude of their difference is $\sqrt{3}$.

Check whether the following vectors are anti-parallel or not.

$\overrightarrow{a}=-2\hat{i}-4\hat{j}\text{ and }\overrightarrow{b}=\hat{i}+2\hat{j}$.

The position vectors of two points $A$ and $B$ are $\overline{\mathrm{OA}}=2\hat{i}-\hat{j}-\hat{k}$ and $\overline{\mathrm{OB}}=2\hat{\mathrm{i}}-\hat{\mathrm{j}}+2\hat{\mathrm{k}}$, respectively. The position vector of a point $P$ which divides the line segment joining $A$ and $B$ in the ratio $7:1$ internally is

The position vectors of two points $A$ and $B$ are $\overline{\mathrm{OA}}=2\hat{i}-\hat{j}-\hat{k}$ and $\overline{\mathrm{OB}}=2\hat{\mathrm{i}}-\hat{\mathrm{j}}+2\hat{\mathrm{k}}$, respectively. The position vector of a point $P$ which divides the line segment joining $A$ and $B$ in the ratio $2:1$ is

$\overrightarrow{a}=(2,4,6) \text{ and }\overrightarrow{b}=(1,2,3)$ 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 $\overrightarrow{a}+\overrightarrow{b}$.

If the projection of $\overrightarrow{a}=\hat{i}-2\hat{j}+3\hat{k}\text{ on }\overrightarrow{b}=2\hat{i}+\lambda \hat{k}$ is zero, then the value of $\lambda$ is