ABCDEF is a regular hexagon and forces repres | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the resultant force be $\vec{R} = \overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AD} + \overrightarrow{AE} + \overrightarrow{AF}$

Vedclass · Accepted Answer

$3\, \overrightarrow{AD}$

Vedclass · Answer

(C) Let the resultant force be $\vec{R} = \overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AD} + \overrightarrow{AE} + \overrightarrow{AF}$.In a regular hexagon $ABCDEF$,the center $O$ is the midpoint of the diagonals $AD$,$BE$,and $CF$. Thus,$\overrightarrow{AB} + \overrightarrow{AE} = 2\overrightarrow{AO} = \overrightarrow{AD}$ (since $\overrightarrow{AD} = 2\overrightarrow{AO}$).Similarly,$\overrightarrow{AC} + \overrightarrow{AF} = 2\overrightarrow{AO} = \overrightarrow{AD}$.Substituting these into the expression for $\vec{R}$:$\vec{R} = (\overrightarrow{AB} + \overrightarrow{AE}) + (\overrightarrow{AC} + \overrightarrow{AF}) + \overrightarrow{AD}$$\vec{R} = \overrightarrow{AD} + \overrightarrow{AD} + \overrightarrow{AD} = 3\overrightarrow{AD}$.

$ABCDEF$ is a regular hexagon and forces represented in magnitude and direction by $\overrightarrow{AB}, \overrightarrow{AC}, \overrightarrow{AD}, \overrightarrow{AE}$ and $\overrightarrow{AF}$ act at point $A$. Their resultant is:

Similar Questions

How is the magnitude of a vector quantity represented?

$ABC$ is an equilateral triangle. The length of each side is $a$ and the centroid is point $O$. Then $\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC} = \dots$

Identify the false statement regarding the magnetic properties of substances.

When a particle moves from point $A(2,2,3)$ to point $B(6,6,9)$,its displacement vector is

Given $A = 3\hat{i} + 4\hat{j}$ and $B = 7\hat{i} + 24\hat{j}$,find a vector that has the same magnitude as $B$ and is parallel to $A$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module