Mathematics in Physics

JEE Main level, single correct, medium

11 of 121

Question 11 of 121

A vector in x−yx-y plane makes an angle of 30o{30}^{o} with yy-axis. The magnitude of yy-component of vector is 232\sqrt{3}. The magnitude of xx-component of the vector will be :

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Answer: (C) 22

The angle made by the vector on xaxisxaxis is
θ=90∘−30∘=60∘\theta =90^{\circ}-30^{\circ}=60^{\circ}
Let the vector be a⃗\vec{a}.
It is given that
ay=23⇒asin⁡60∘=23⇒a32=23⇒a=4{a}_{y}=2\sqrt{3} \Rightarrow a\sin 60^{\circ}=2\sqrt{3} \Rightarrow \dfrac{a\sqrt{3}}{2}=2\sqrt{3} \Rightarrow a=4
xx component is ax=acos⁡60∘⇒ax=4×12=2{a}_{x}=a\cos 60^{\circ} \Rightarrow {a}_{x}=4\times \dfrac{1}{2}=2

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