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 $\overrightarrow{\mathrm{R}},|\overrightarrow{\mathrm{R}}| \leq|\overrightarrow{\mathrm{A}}|+|\overrightarrow{\mathrm{B}}|$
What vector must be added to the two vectors $\hat i - 2\hat j + 2\hat k$ and $2\hat i + \hat j - \hat k,$ so that the resultant may be a unit vector along $X-$axis
The resultant of two forces $3P$ and $2P$ is $R$. If the first force is doubled then the resultant is also doubled. The angle between the two forces is ........... $^o$
Let $\overrightarrow C = \overrightarrow A + \overrightarrow B $ then
$\overrightarrow A \, = \,3\widehat i\, + \,2\widehat j$ , $\overrightarrow B \, = \widehat {\,i} + \widehat j - 2\widehat k$ then find their addition by algebric method.
Unit vector parallel to the resultant of vectors $\vec A = 4\hat i - 3\hat j$and $\vec B = 8\hat i + 8\hat j$ will be