Question # A unit radial vector ( hat{r} ) makes angles of ( alpha=30^{circ} ) relative to the ( mathrm{x} ) -axis, ( beta=60^{circ} ) relative to the y-axis, and ( gamma=90^{circ} ) relative to the z-axis. The vector ( hat{r} ) can be written as:

# A unit radial vector ( hat{r} ) makes angles of ( alpha=30^{circ} ) relative to the ( mathrm{x} ) -axis, ( beta=60^{circ} ) relative to the y-axis, and ( gamma=90^{circ} ) relative to the z-axis. The vector ( hat{r} ) can be written as:

(1) ( frac{1}{2} hat{i}+frac{sqrt{3}}{2} hat{j} )

(2) ( frac{sqrt{3}}{2} hat{i}+frac{1}{2} hat{j} )

(3) ( frac{sqrt{2}}{3} hat{mathrm{i}}+frac{1}{sqrt{3}} )

(4) None of these

Solution

( stackrel{}{operatorname{ginen} alpha=30^{circ}}, beta=60^{circ} cdotleft(y=90^{circ}right) )

fithers in ( x ) -yplane

[

begin{aligned}

therefore text { vector } &=1 cos alpha hat{i}+1 cos beta hat{j}

& Rightarrow frac{sqrt{3}}{2} hat{imath}+frac{1}{2} hat{jmath}

end{aligned}

]