Explain subtraction of vectors.
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).
Similar Questions
If $\vec{P}+\vec{Q}=\overrightarrow{0}$, then which of the following is necessarily true?
If $\vec{P}+\vec{Q}=\overrightarrow{0}$, then which of the following is necessarily true?
$100$ coplanner forces each equal to $10\,\,N$ act on a body. Each force makes angle $\pi /50$ with the preceding force. What is the resultant of the forces.......... $N$
$100$ coplanner forces each equal to $10\,\,N$ act on a body. Each force makes angle $\pi /50$ with the preceding force. What is the resultant of the forces.......... $N$
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 ?
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 ?
A particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously (Assuming particle is initially at rest)
${\vec F_1} = 5\hat i - 5\hat j + 5\hat k$ ${\vec F_2} = 2\hat i + 8\hat j + 6\hat k$
${\vec F_3} = - 6\hat i + 4\hat j - 7\hat k$ ${\vec F_4} = - \hat i - 3\hat j - 2\hat k$
Then the particle will move
A particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously (Assuming particle is initially at rest)
${\vec F_1} = 5\hat i - 5\hat j + 5\hat k$ ${\vec F_2} = 2\hat i + 8\hat j + 6\hat k$
${\vec F_3} = - 6\hat i + 4\hat j - 7\hat k$ ${\vec F_4} = - \hat i - 3\hat j - 2\hat k$
Then the particle will move
Prove the associative law of vector addition.
Prove the associative law of vector addition.