Basics of Vectors

The magnitudes of vectors  $\overrightarrow{A},\overrightarrow{B}\mathrm{and}\overrightarrow{C}$  are $3,$ $4$ and $5$ units respectively. If  $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$ , then the angle between  $\overrightarrow{A}\mathrm{and}\overrightarrow{B}$  is :

If $\overrightarrow{a}=\overrightarrow{AB} \& \overrightarrow{b}=\overrightarrow{BC}$ are two adjacent sides of a regular hexagon $ABCDEF,$ find the vectors $\overrightarrow{CD}, \overrightarrow{DE}, \overrightarrow{EF}, \overrightarrow{AE} \& \overrightarrow{CE}$ in terms of $\overrightarrow{a} \& \overrightarrow{b}.$

Vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are non-collinear. For what value of $\alpha$ are the vectors $\overrightarrow{u}=\left(\alpha -2\right)\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{v}=\left(2+3\alpha \right)\overrightarrow{a}-3\overrightarrow{b}$ collinear?

Find the magnitude of the following free vector $\overrightarrow{X}=-6\hat{i}-3\hat{j}-2\hat{k}$.

Find the magnitude of the following free vector $\overrightarrow{X}=-2\hat{i}+3\hat{j}+6\hat{k}$.

Find the magnitude of the following free vector $\overrightarrow{a}=2\hat{i}+\hat{j}+2\hat{k}$

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

$\overrightarrow{a}=-4\hat{i}-8\hat{j}\text{ and }\overrightarrow{b}=\hat{i}+2\hat{j}$.

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

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

Define Anti-parallel Vectors and give one example.

Define Localised Vector and give one example.

Define free vector and give one example.

Which triangle is formed by the points whose position vectors are $4\overrightarrow{i}-3\overrightarrow{j}+\overrightarrow{k}, 2\overrightarrow{i}-4\overrightarrow{j}+5\overrightarrow{k}, \overrightarrow{i}-\overrightarrow{j}$?

Which triangle is formed by the points whose position vectors are $4\overrightarrow{i}-3\overrightarrow{j}+\overrightarrow{k}, 2\overrightarrow{i}-4\overrightarrow{j}+5\overrightarrow{k}, \overrightarrow{i}-\overrightarrow{j}$?

Select the scalar quantity from the list given below:

Displacement, weight, work, acceleration, force

Why weight is considered as a vector quantity?

Mass is a vector quantity.

Find the value of $m-n$ given that the vectors $5\hat{i}+2\hat{j}$ and $m\hat{i}+n\hat{j}$ are equal.

A vector of magnitude $5$ units along the vector $\hat{i}-2\hat{j}+2\hat{k}$ is