Prove the associative law of vector addition.
Prove the associative law of vector addition.
Consider the vectors of shown in the figure. To find the associative law of $\vec{A}, \vec{B}$ and $\vec{C}$ Draw $\vec{A}=\overrightarrow{O P}, \vec{B}=\overrightarrow{P Q}$ and $\vec{C}=\overrightarrow{Q R}$
By triangle law of vector we get, Figure $(b)$
From the figure $\Delta \mathrm{OPQ}$
$\rightarrow \quad \rightarrow \quad \rightarrow \quad \rightarrow$
$\mathrm{A}+\mathrm{B}=\mathrm{OP}+\mathrm{PQ}$
$\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{OQ}}$
By adding $\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{QR}}$ in both the sides
$(\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}})+\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{OQ}}+\overrightarrow{\mathrm{QR}}$
We get $\quad(\vec{A}+\vec{B})+\vec{C}=\overrightarrow{O R} \ldots \ldots$ $(i)$
Similar Questions
Three girls skating on a circular ice ground of radius $200 \;m$ start from a point $P$ on the edge of the ground and reach a point $Q$ diametrically opposite to $P$ following different paths as shown in Figure. What is the magnitude of the displacement vector for each ? For which girl is this equal to the actual length of path skate ?
Three girls skating on a circular ice ground of radius $200 \;m$ start from a point $P$ on the edge of the ground and reach a point $Q$ diametrically opposite to $P$ following different paths as shown in Figure. What is the magnitude of the displacement vector for each ? For which girl is this equal to the actual length of path skate ?
Two forces of $12 \,N$ and $8 \,N$ act upon a body. The resultant force on the body has maximum value of........$N$
Two forces of $12 \,N$ and $8 \,N$ act upon a body. The resultant force on the body has maximum value of........$N$
$\overrightarrow A \, = \,2\widehat i\, + \,3\widehat j + 4\widehat k$ , $\overrightarrow B \, = \widehat {\,i} - \widehat j + \widehat k$, then find their substraction by algebric method.
$\overrightarrow A \, = \,2\widehat i\, + \,3\widehat j + 4\widehat k$ , $\overrightarrow B \, = \widehat {\,i} - \widehat j + \widehat k$, then find their substraction by algebric method.
Explain the analytical method for vector addition.
Explain the analytical method for vector addition.
On an open ground, a motorist follows a track that turns to his left by an angle of $60^{°}$ after every $500\; m$. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.
On an open ground, a motorist follows a track that turns to his left by an angle of $60^{°}$ after every $500\; m$. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.