MCQ
Find angle between $\vec A = 3\hat i - \hat j + 4\hat k$ and $Z-$ axis
  • A
    ${\tan ^{ - 1}}\,\left( {\frac{{\sqrt {22} }}{4}} \right)$
  • ${\tan ^{ - 1}}\,\left( {\frac{{\sqrt {10} }}{4}} \right)$
  • C
    ${\sin ^{ - 1}}\,\left( {\frac{{\sqrt {10} }}{4}} \right)$
  • D
    ${\sin ^{ - 1}}\,\left( {\frac{4}{{\sqrt {26} }}} \right)$

Answer

Correct option: B.
${\tan ^{ - 1}}\,\left( {\frac{{\sqrt {10} }}{4}} \right)$
b
$\cos \theta=\frac{\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}}{\mathrm{AB}}=\frac{(3 \hat{\mathrm{i}}-\hat{j}+4 \hat{\mathrm{k}}) \cdot(\hat{\mathrm{k}})}{\sqrt{(3)^{2}+(-1)^{2}+(4)^{2}} \sqrt{(1)^{2}}}=\frac{4}{\sqrt{26}}$

Base $=4,$ hypotenuse $=\sqrt{26} \cdot$ perpendicular $=\sqrt{10}$

$\tan \theta=\frac{\sqrt{10}}{4}, \quad \theta=\tan ^{-1}\left(\frac{\sqrt{10}}{4}\right)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

An object of mass $m$ is sliding down a hill of arbitrary shape and after traveling a certain horizontal path stops because of friction. The friction coefficient is different for different segments of the entire path but it is independent of the velocity and direction of motion. The work done that a force must perform to return the object  its initial position along the same path would be :-
Water falls from a tap, down the streamline
A sample of an ideal gas occupies a volume $V$ at a pressure $P$ and absolute temperature $T,$ the mass of each molecule is $m.$ The expression for the density of gas is ($k =$ Boltzmann’s constant)
A couple is acting on a two particle systems. The resultant motion will be:
Two, spring $P$ and $Q$ of force constants $k_p$ and ${k_Q}\left( {{k_Q} = \frac{{{k_p}}}{2}} \right)$ are stretched by applying forces of equal magnitude. If the energy stored in $Q$ is $E$, then the energy stored in $P$ is
Which one of the following statements is true?
An aeroplane flying $490 \,m$ above ground level at $100\, m/s$, releases a block. How far on ground will it strike ......... $km$
The speed of a wave in a certain medium is $960\, m/s$. If $3600$ waves pass over a certain point of the medium in $1\, minute$, the wavelength is  .... $metres$
A book lying on a table is an example of:
A body of mass $5\,kg$ rests on a rough horizontal surface of coefficient of friction $0.2.$ The body is pulled through a distance of $10\,m$ by a horizontal force of $25\, N$. The kinetic energy acquired by it is ......... $J$