Embibe Experts Solutions for Chapter: Vector Algebra, Exercise 1: Chhattisgarh Board-2018

Find the area of the parallelogram whose two adjacent sides are represented by the vectors $\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k}$ and $\overrightarrow{b}=3\hat{i}-4\hat{j}-\hat{k}$.

Three forces acting on a particle are in equilibrium. If the angle between first two forces is $90°$ and angle between second and third is $120°$, then find the ratio of the forces.

The resultant of two forces $P$ and $Q$ is $R$. If $Q$ is doubled, then the new resultant will be perpendicular to $P$. Prove that $Q=R$.

Find the magnitude of vector $\overrightarrow{a}=2\hat{i}-7\hat{j}-3\hat{k}$.

Prove that: $\left[\begin{array}{lll}\overrightarrow{a}-\overrightarrow{b}& \overrightarrow{b}-\overrightarrow{c}& \overrightarrow{c}-\overrightarrow{a}\end{array}\right]=0$

The force of $6$ units works parallel to the vector $2\hat{i}-2\hat{j}+\hat{k}$ and displaces one particle from $\hat{i}+2\hat{j}+3\hat{k}$ to $5\hat{i}+3\hat{j}+7\hat{k}.$ Find out the work-done by force.

Find the area of the parallelogram whose diagonals are $\overline{a}=3i+j-2k\text{ and }\overline{b}=i-3j+4k$.

Find the value of $\hat{i}·(\hat{j}\times \hat{k})+\hat{j}·(\hat{i}\times \hat{k})+\hat{k}·(\hat{i}\times \hat{j})$.