Resolution of Vectors

Represent the vector $\overrightarrow{A}=3\hat{i}+4\hat{j}+6\hat{k}$  in matrix form.

Represent the vector $\overrightarrow{A}=2\hat{i}+4\hat{j}+6\hat{k}$  in matrix form.

Represent the vector $\overrightarrow{A}=2\hat{i}+4\hat{j}+5\hat{k}$  in matrix form.

Represent the vector $\overrightarrow{A}=2\hat{i}+3\hat{j}+5\hat{k}$  in matrix form.

Represent the vector $\overrightarrow{A}=2\hat{i}+3\hat{j}+4\hat{k}$  in matrix form.

Find the direction cosines of vector $6\hat{i}-7\hat{j}+8\hat{k}$.

Find the direction cosines of vector $6\hat{i}-4\hat{j}+2\hat{k}$.

Find the direction cosines of vector $6\hat{i}-5\hat{j}+7\hat{k}$.

Find the direction cosines of vector $4\hat{i}-5\hat{j}+3\hat{k}$.

Find the direction cosines of vector $5\hat{i}-3\hat{j}+4\hat{k}$.

Vector $\overrightarrow{P}=6\hat{i}+4\sqrt{2}\hat{j}+4\sqrt{2}\hat{k}$ makes angle from $Z$-axis equal to

A vector $\overrightarrow{a}$ has components $2p$ and $1$ with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counterclockwise sense. If, with respect to the new system,$\overrightarrow{a}$ has components $p+1$ and  $1$, then

What is the vertical component of a $5\mathrm{N}$ force acting on a particle along a direction making an angle of $60°$ with vertical?

What are the value of the angles which a vector $\hat{\mathrm{i}}+\hat{\mathrm{j}}+\sqrt{2}\hat{\mathrm{k}}$ makes with $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ axes respectively ?

Given three vectors $\overrightarrow{a }=6 \hat{i}-3 \hat{j}$, $\overrightarrow{b }=2 \hat{i}-6 \hat{j}$ and $\overrightarrow{c }= -2 \hat{i}+21 \hat{j}$ such that $\overrightarrow{\alpha }=\overrightarrow{a }+\overrightarrow{b }+\overrightarrow{c }$. Then the resolution of the vector $\overrightarrow{\alpha }$ into components with respect to $\overrightarrow{a }$and $\overrightarrow{b }$is given by :

A bird flies at an angle of ${60}^o$ to the horizontal. Its horizontal component of velocity is $10 {\text{m s}}^{-1}.$ Find the vertical component of velocity in ${\text{m s}}^{-1}.$

The magnitude of resultant of three vectors of magnitude 1, 2 and 3 whose directions are those of the sides of an equilateral triangle taken in order is

If projection of any line on coordinate axes$3, 4$ and $5$, then its length is