Odisha Board Solutions for Chapter: Scalars and Vectors, Exercise 1: MODEL QUESTIONS

The minimum number of unequal forces whose vector sum can be zero is

The component of $9\hat{\mathrm{i}}+17\hat{\mathrm{k}}$ along $\mathrm{z}$ -axis is:

The magnitude of vector product of two vectors is $\sqrt{3}$ times their scalar product. The angle between the vectors is

Given, $\overrightarrow{P}=3\hat{i}+4\hat{j}-2\hat{k}, \overrightarrow{Q}=4\hat{i}-3\hat{j}+2\hat{k}$ unit vector in the direction of $\overrightarrow{P}+\overrightarrow{Q}$ is.

If $\mathrm{AB}$ be the diameter of a circle and $\mathrm{C}$ is any point on the circumference of the circle. Prove by vector method that angle $\mathrm{ACB}$ is right angle.

The diagonals of a parallelogram are represented by ${\overrightarrow{\mathrm{R}}}_1=3\hat{\mathrm{i}}-2\hat{\mathbf{j}}+7\hat{\mathrm{k}}, {\overrightarrow{\mathrm{R}}}_2=5\hat{\mathrm{i}}+6\hat{\mathrm{j}}-3\hat{\mathrm{k}}$, find the area of the parallelogram.

A particle gets displaced through $\hat{\mathrm{i}}+2\hat{\mathrm{j}}-4\hat{\mathrm{k}}$ due to a force $2\hat{\mathrm{i}}-3\hat{\mathrm{j}}-6\hat{\mathrm{k}}$. The displacement and force are measured in S.I. units. Find the work done.

Show that $\overrightarrow{A}·\overrightarrow{B}=\frac{1}{4}\left[|\overrightarrow{A}+\overrightarrow{B}{|}^2-|\overline{A}-\overrightarrow{B}{|}^2\right]$.