The resultant of two vectors at an angle 150^ | vedclass

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(B) Let the two vectors be $\vec{A}$ and $\vec{B}$. The resultant $\vec{R}$ is perpendicular to $\vec{A}$.Given,the angle between $\vec{A}$ and $\vec{

Vedclass · Accepted Answer

$10 \sqrt{3}$

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(B) Let the two vectors be $\vec{A}$ and $\vec{B}$. The resultant $\vec{R}$ is perpendicular to $\vec{A}$.Given,the angle between $\vec{A}$ and $\vec{B}$ is $150^{\circ}$.From the geometry of the vector triangle,the angle between $\vec{R}$ and $\vec{B}$ is $180^{\circ} - 150^{\circ} = 30^{\circ}$.In the right-angled triangle formed by $\vec{A}$,$\vec{B}$,and $\vec{R}$,we have:$	an 30^{\circ} = \frac{R}{A} \Rightarrow \frac{1}{\sqrt{3}} = \frac{10}{A} \Rightarrow A = 10\sqrt{3}$.Also,$\sin 30^{\circ} = \frac{R}{B} \Rightarrow \frac{1}{2} = \frac{10}{B} \Rightarrow B = 20$.The magnitudes are $A = 10\sqrt{3} \approx 17.32$ and $B = 20$. The smaller vector is $\vec{A}$ with magnitude $10\sqrt{3}$.

The resultant of two vectors at an angle $150^{\circ}$ is $10$ units and is perpendicular to one vector. The magnitude of the smaller vector is ....... units

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