Explain subtraction of vectors.
Subtraction of vectors can be defined in terms of addition of vectors.
We define the difference of two vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ as the sum of two vectors $\overrightarrow{\mathrm{A}}$ and $-\overrightarrow{\mathrm{B}}$.
$\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{A}}+(-\overrightarrow{\mathrm{B}})$
Thus, substraction of vectors means adding opposite of a vector in another vector.
In figure (a), $\vec{A}, \vec{B}$ and $-\vec{B}$ is represented.
In figure (b), $-\vec{B}$ is added to $\vec{A}$.
By triangle method for vector addition,
$\overrightarrow{\mathrm{R}_{2}}=\overrightarrow{\mathrm{A}}+(-\overrightarrow{\mathrm{B}})$
$\therefore\overrightarrow{\mathrm{R}_{2}}=\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}$
(For comparison, $\overrightarrow{\mathrm{R}_{1}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$ is shown).
The ratio of maximum and minimum magnitudes of the resultant of two vector $\vec a$ and $\vec b$ is $3 : 1$. Now $| \vec a |$ is equal to
The sum of three forces ${\vec F_1} = 100\,N,{\vec F_2} = 80\,N$ and ${\vec F_3} = 60\,N$ acting on a particle is zero. The angle between $\vec F_1$ and $\vec F_2$ is nearly .......... $^o$
Given $a+b+c+d=0,$ which of the following statements eare correct:
$(a)\;a, b,$ c, and $d$ must each be a null vector,
$(b)$ The magnitude of $(a+c)$ equals the magnitude of $(b+d)$
$(c)$ The magnitude of a can never be greater than the sum of the magnitudes of $b , c ,$ and $d$
$(d)$ $b + c$ must lie in the plane of $a$ and $d$ if $a$ and $d$ are not collinear, and in the line of a and $d ,$ if they are collinear ?
Three forces given by vectors $2 \hat{i}+2 \hat{j}, 2 \hat{i}-2 \hat{j}$ and $-4 \hat{i}$ are acting together on a point object at rest. The object moves along the direction
Two forces are such that the sum of their magnitudes is $18\; N$ and their resultant is $12\; N$ which is perpendicular to the smaller force. Then the magnitudes of the forces are