(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 1 Motion in a Plane: Vectors Resolution of a Vector into Rectangular Components

Easy

$A$ 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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1 Motion in a Plane: Vectors

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Resolution of a Vector into Rectangular Components

The projection of a vector $\vec{r} = 3\hat{i} + \hat{j} + 2\hat{k}$ on the $xy$-plane has magnitude:

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$A$ person pushes a box kept on a horizontal surface with a force of $100\,N$ as shown in the figure. In unit vector notation,the force $\vec{F}$ can be expressed as?

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Explain the resolution of a vector in three dimensions.

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Any vector in an arbitrary direction can always be replaced by two (or three)

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The $y$-component of vector $\vec{A}$ is $+3.0 \ m$. If $\vec{A}$ makes an angle of $30^{\circ}$ counterclockwise from the positive $y$-axis, the magnitude of $\vec{A}$ is (assume $\vec{A}$ is in the $x-y$ plane).

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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 .........

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The projection of a vector $\vec{r} = 3\hat{i} + \hat{j} + 2\hat{k}$ on the $xy$-plane has magnitude:

$A$ person pushes a box kept on a horizontal surface with a force of $100\,N$ as shown in the figure. In unit vector notation,the force $\vec{F}$ can be expressed as?

Explain the resolution of a vector in three dimensions.

Any vector in an arbitrary direction can always be replaced by two (or three)

The $y$-component of vector $\vec{A}$ is $+3.0 \ m$. If $\vec{A}$ makes an angle of $30^{\circ}$ counterclockwise from the positive $y$-axis, the magnitude of $\vec{A}$ is (assume $\vec{A}$ is in the $x-y$ plane).

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