(A) Given,magnitude of displacement vector $|\vec{d}| = 4$ and angle $\theta = 30^{\circ}$ with the $x$-axis.The rectangular components of a vector $\

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(A) Given,magnitude of displacement vector $|\vec{d}| = 4$ and angle $\theta = 30^{\circ}$ with the $x$-axis.The rectangular components of a vector $\vec{d}$ are given by:$d_x = |\vec{d}| \cos \theta$$d_y = |\vec{d}| \sin \theta$Substituting the values:$d_x = 4 \cos 30^{\circ} = 4 \times \frac{\sqrt{3}}{2} = 2\sqrt{3}$$d_y = 4 \sin 30^{\circ} = 4 \times \frac{1}{2} = 2$Thus,the rectangular components are $2\sqrt{3}$ and $2$.

Class 11 Physics 3-1.Vectors Resolution of a Vector into Rectangular Components

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$A$ displacement vector of magnitude $4$ makes an angle $30^{\circ}$ with the $x$-axis. Its rectangular components in the $x-y$ plane are .........

A
$2 \sqrt{3}, 2$
B
$4 \sqrt{3}, 4$
C
$\frac{2}{\sqrt{3}}, 2$
D
$\frac{4}{\sqrt{3}}, 4$

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Resolution of a Vector into Rectangular Components

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$A$ displacement vector of magnitude $4$ makes an angle $30^{\circ}$ with the $x$-axis. Its rectangular components in the $x-y$ plane are .........

Similar Questions

If the magnitude of a vector $\overrightarrow{p}$ is $25 \text{ units}$ and its $y$-component is $7 \text{ units}$, then its $x$-component is (in $\text{ units}$)

What is the maximum number of rectangular components into which a vector can be split in space?

$A$ plane covers $500 \,m$ in a direction $60^o$ with the runway while starting the flight. Find the distance covered by the plane in the horizontal and vertical directions.

$A$ person walks $25.0^{\circ}$ north of east for $3.18 \,km$. How far would she have to walk due north and then due east to arrive at the same location?

What is the component of $3\hat{i} + 4\hat{j}$ along $\hat{i} + \hat{j}$?

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