MCQ
If a unit vector is represented by $0.5\hat{\text{i}}+0.8\hat{\text{j}}+\text{c}\hat{\text{k}},$ then the value of $'c\ '$ is:
  • A
    $1$
  • $\sqrt{0.11}$
  • C
    $\sqrt{0.01}$
  • D
    $\sqrt{0.39}$

Answer

Correct option: B.
$\sqrt{0.11}$
Here,$(0.5)^2 + (0.8)^2 + (c)^2 = 1$
or $\text{c}=\sqrt{0.11}$

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

Two satellites of earth $S_1$ and $S_2$ are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2$. Which one of the following statement is true ?
A particle is acted simultaneously by mutually perpendicular simple hormonic motions $\text{x}=\text{a}\cos\omega\text{t}$ and $\text{y}=\text{a}\sin\omega\text{t}.$ The trajectory of motion of the particle will be:
The gravitational field due to a mass distribution is $E = K/{x^3}$ in the $X-$direction. ($K$ is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance $X$ is
Kepler discovered
Four spheres, each of mass $M$ and radius $\omega $are situated at the four corners of square of side $R$. The moment of inertia of the system about an axis perpendicular to the plane of square and passing through its centre will be      
For a ball falling in a liquid with constant velocity, ratio of resistance force due to the liquid to that due to gravity is:
An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature $T _1$, pressure $P_1$ and volume $V_1$ and the spring is in its relaxed state. The gas is then heated very slowly to temperature $T_2$, pressure $P _2$ and volume $V _2$. During this process the piston moves out by a distance $x$. Ignoring the friction between the piston and the cylinder, the correct statement$(s)$ is(are)

$(A)$ If $V_2=2 V_1$ and $T_2=3 T_1$, then the energy stored in the spring is $\frac{1}{4} P_1 V_1$

$(B)$ If $V_2=2 V_1$ and $T_2=3 T_1$, then the change in internal energy is $3 P_1 V_1$

$(C)$ If $V_2=3 V_1$ and $T_2=4 T_1$, then the work done by the gas is $\frac{7}{3} P_1 V_1$

$(D)$ If $V_2=3 V_1$ and $T_2=4 T_1$, then the heat supplied to the gas is $\frac{17}{6} P_1 V_1$

The acceleration $a$ (in $ms ^{-2}$ ) of a body, starting from rest varies with time $t$ (in second) according to the relation $a=3 t+4$. The velocity of the body starting from rest at time $t=2 s$ will be $........ms ^{-1}$
A stone projected at an angle of $60^o$ from the ground level strikes at an angle of $30^o$ on the roof of a building of height $‘h= 30\,m ’$ . Find the speed of projection(in $m/s$ ) of the stone
Two bodies $A$ (of mass $1\,kg$) and $B$ (of mass $3\,kg$) are dropped from heights of $16\,m$ and $25\,m$ respectively . The ratio of the time taken by them to reach the ground is