(C) The resultant of $2$ vectors $\vec{A}$ and $\vec{B}$ is given by $\vec{R} = \vec{A} + \vec{B}$.For the resultant to be zero,$\vec{A} + \vec{B} = 0

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Yes,when the $2$ vectors are same in magnitude but opposite in sense.

(C) The resultant of $2$ vectors $\vec{A}$ and $\vec{B}$ is given by $\vec{R} = \vec{A} + \vec{B}$.For the resultant to be zero,$\vec{A} + \vec{B} = 0$,which implies $\vec{A} = -\vec{B}$.This means the two vectors must have the same magnitude $(|A| = |B|)$ but must be directed in opposite directions (an angle of $180^{\circ}$ or $\pi$ radians between them).Therefore,the correct condition is that the $2$ vectors are same in magnitude but opposite in sense.

Class 11 Physics 3-1.Vectors Addition and Subtraction of Vectors

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Can the resultant of $2$ vectors be zero?

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A
Yes,when the $2$ vectors are same in magnitude and direction.
B
No.
C
Yes,when the $2$ vectors are same in magnitude but opposite in sense.
D
Yes,when the $2$ vectors are same in magnitude making an angle of $\frac{2\pi}{3}$ with each other.

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3-1.Vectors

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Addition and Subtraction of Vectors

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The magnitudes of vectors $\overrightarrow{A}$,$\overrightarrow{B}$,and $\overrightarrow{C}$ are $12$,$5$,and $13$ units respectively,and $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$. Then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

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The three vectors $\vec A = 3\hat i - 2\hat j + \hat k$,$\vec B = \hat i - 3\hat j + 5\hat k$,and $\vec C = 2\hat i + \hat j - 4\hat k$ form:

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Given $|\vec{P}| > |\vec{Q}|$. What is the angle between their maximum resultant vector and minimum resultant vector (in $^{\circ}$)?

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If $\overrightarrow A = 2\hat i + \hat j$,$\overrightarrow B = 3\hat j - \hat k$,and $\overrightarrow C = 6\hat i - 2\hat k$,find the value of $\overrightarrow A - 2\overrightarrow B + 3\overrightarrow C$.

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There are five vectors,each of magnitude $8$ units. These vectors form a regular pentagon as shown in the figure. Find the magnitude of the resultant vector.

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Can the resultant of $2$ vectors be zero?

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The magnitudes of vectors $\overrightarrow{A}$,$\overrightarrow{B}$,and $\overrightarrow{C}$ are $12$,$5$,and $13$ units respectively,and $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$. Then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

The three vectors $\vec A = 3\hat i - 2\hat j + \hat k$,$\vec B = \hat i - 3\hat j + 5\hat k$,and $\vec C = 2\hat i + \hat j - 4\hat k$ form:

Given $|\vec{P}| > |\vec{Q}|$. What is the angle between their maximum resultant vector and minimum resultant vector (in $^{\circ}$)?

If $\overrightarrow A = 2\hat i + \hat j$,$\overrightarrow B = 3\hat j - \hat k$,and $\overrightarrow C = 6\hat i - 2\hat k$,find the value of $\overrightarrow A - 2\overrightarrow B + 3\overrightarrow C$.

There are five vectors,each of magnitude $8$ units. These vectors form a regular pentagon as shown in the figure. Find the magnitude of the resultant vector.

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