Three forces of 3 N,4 N,and 12 N act on a | vedclass

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Question

(B) Since the forces are mutually perpendicular,we can represent them as vectors along the $x$,$y$,and $z$ axes:$\vec{F}_1 = 3\hat{i} \ N$,$\vec{F}_2

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(B) Since the forces are mutually perpendicular,we can represent them as vectors along the $x$,$y$,and $z$ axes:$\vec{F}_1 = 3\hat{i} \ N$,$\vec{F}_2 = 4\hat{j} \ N$,and $\vec{F}_3 = 12\hat{k} \ N$.The resultant force vector is given by the sum of these vectors:$\vec{F} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 = 3\hat{i} + 4\hat{j} + 12\hat{k}$.The magnitude of the resultant force is calculated using the formula $F = \sqrt{F_x^2 + F_y^2 + F_z^2}$:$F = \sqrt{3^2 + 4^2 + 12^2} = \sqrt{9 + 16 + 144} = \sqrt{169} = 13 \ N$.

Three forces of $3 \ N$,$4 \ N$,and $12 \ N$ act on a point in mutually perpendicular directions. The magnitude of the resultant force is ........ $N$.

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