Find angle between A = 3 i - j + 4 k and Z- axis - Vidyadip

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

Explore more

More "M.C.Q (1 Marks)" from 3.1 vectors→3.1 vectors — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The planes of two rigid discs are perpendicular to each other. They are rotating about their axes. If their angular velocities are $3 \,rad/sec$ and $4\, rad/sec$ respectively, then the resultant angular velocity of the system would be ........ $rad/sec$

Boiling water is changing into steam. Under this condition, the specific heat of water is

The left end of a massless stick with length $l$ is placed on the corner of a table, as shown in Fig. A point mass $m$ is attached to the center of the stick, which is initially held horizontal. It is then released. Immediately afterward, what normal force does the table exert on the stick?

Two persons of equal height are carrying a long uniform wooden beam of length $\ell $. They are at distance $\frac{\ell }{5}$ and $\frac{\ell }{3}$ . From nearest end of the rod. The ratio of normal reaction at their heads is

The intensity of sound during the festival season increased by $100$ times. This could imply a decibel $(dB)$ level rise from

An ideal monoatomic gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2\, V$ and a final pressure $P_i$. If the same gas is expanded adiabatically to a volume $2\,V$, the final pressure is $P_a$ . The ratio $\frac{{{P_a}}}{{{P_i}}}$ is

A solid ball is completely immersed in a liquid. The coefficients of volume expansion of the ball and liquid are $3 × 10^{-6}$ and $8 × 10^{-6} per ^o C$ respectively. The percentage change in upthrust when the temperature is increased by $100 ^o C$ is ....... $\%$

If the block $A$ & $B$ are moving towards each other with acceleration $a$ and $b$. Find the net acceleration of $C$.

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

Two rods $A$ and $B$ of same cross-sectional are $A$ and length $l$ connected in series between a source $(T_1 = 100^o C)$ and a sink $(T_2 = 0^o C)$ as shown in figure. The rod is laterally insulated If $G_A$ and $G_B$ are the temperature gradients across the rod $A$ and $B$, then