Explain the parallelogram method for vector addition. Also explain that this is comparable to triangle method.
Explain the parallelogram method for vector addition. Also explain that this is comparable to triangle method.
$\vec{A}$ and $\vec{B}$ are to be added as shown in figure $(a).$
Select a point $\mathrm{O}$ as shown in figure $(b)$.
Represent $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ such that their lengths and directions remain unchanged and their tails remain at $\mathrm{O}$.
Draw a parallelogram $\square^{\mathrm{m}}$ OPSQ in which $\vec{A}$ and $\vec{B}$ are adjacent sides of it. Draw a diagonal OS from $\mathrm{O}$.
Vector $\overrightarrow{\mathrm{OS}}$ represent resultant vector of addition of $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$.
$\overrightarrow{\mathrm{OS}}=\overrightarrow{\mathrm{OP}}+\overrightarrow{\mathrm{OQ}} \quad \therefore \overrightarrow{\mathrm{R}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$
Triangle method for vector addition is shown in figure $(c)$.
If is clear that both methods give equal resultant vector. Hence, both methods are comparable to each other.
Here, magnitude of resultant vector $\overrightarrow{\mathrm{R}},|\overrightarrow{\mathrm{R}}| \leq|\overrightarrow{\mathrm{A}}|+|\overrightarrow{\mathrm{B}}|$
Similar Questions
Let $\overrightarrow C = \overrightarrow A + \overrightarrow B $ then
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If $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$ then magnitude and direction of $\overrightarrow A \, + \overrightarrow B $ will be
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Three concurrent forces of the same magnitude are in equilibrium. What is the angle between the forces Also name the triangle formed by the forces as sides
Three concurrent forces of the same magnitude are in equilibrium. What is the angle between the forces Also name the triangle formed by the forces as sides
Statement $I:$ If three forces $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{3}$ are represented by three sides of a triangle and $\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}$, then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement $II:$ A triangle made up of three forces $\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}$ and $\overrightarrow{{F}}_{3}$ as its sides taken in the same order, satisfy the condition for translatory equilibrium.
In the light of the above statements, choose the most appropriate answer from the options given below:
Statement $I:$ If three forces $\vec{F}_{1}, \vec{F}_{2}$ and $\vec{F}_{3}$ are represented by three sides of a triangle and $\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}$, then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement $II:$ A triangle made up of three forces $\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}$ and $\overrightarrow{{F}}_{3}$ as its sides taken in the same order, satisfy the condition for translatory equilibrium.
In the light of the above statements, choose the most appropriate answer from the options given below:
- [JEE MAIN 2021]
Prove the associative law of vector addition.
Prove the associative law of vector addition.