Give the equations to find the magnitude and | vedclass

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(A) Let two vectors $\vec{A}$ and $\vec{B}$ be represented by two adjacent sides of a parallelogram. The resultant vector $\vec{R} = \vec{A} + \vec{B}

Vedclass · Accepted Answer

Magnitude: $R = \sqrt{A^2 + B^2 + 2AB \cos 	heta}$,Direction: $	an \alpha = \frac{B \sin 	heta}{A + B \cos 	heta}$

Vedclass · Answer

(A) Let two vectors $\vec{A}$ and $\vec{B}$ be represented by two adjacent sides of a parallelogram. The resultant vector $\vec{R} = \vec{A} + \vec{B}$ is given by the diagonal of the parallelogram.$1$. Magnitude of the resultant vector: Using the law of cosines in the triangle formed by the vectors,the magnitude $R$ is given by $R = \sqrt{A^2 + B^2 + 2AB \cos 	heta}$,where $	heta$ is the angle between $\vec{A}$ and $\vec{B}$.$2$. Direction of the resultant vector: If $\alpha$ is the angle that the resultant vector $\vec{R}$ makes with vector $\vec{A}$,then the direction is given by $	an \alpha = \frac{B \sin 	heta}{A + B \cos 	heta}$.

Give the equations to find the magnitude and direction of the resultant vector of two vectors $\vec{A}$ and $\vec{B}$ that are inclined at an angle $\theta$ to each other.

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