A) \[+2\overset{\to }{\mathop{\mathbf{A}}}\,,\,\,0\]
B) \[+\overset{\to }{\mathop{\mathbf{A}}}\,,\,\,0\]
C) \[-\overset{\to }{\mathop{\mathbf{A}}}\,,\,\,0\]
D) \[-2\overset{\to }{\mathop{\mathbf{A}}}\,,\,\,0\]
Correct Answer: D
Solution :
Key Idea: When direction of a vector is reversed it has same magnitude but with minus sign. The value of \[\Delta \overset{\to }{\mathop{\mathbf{A}}}\,=\Delta \overset{\to }{\mathop{{{\mathbf{A}}_{2}}}}\,-\Delta \overset{\to }{\mathop{{{\mathbf{A}}_{1}}}}\,\] Given, \[\overset{\to }{\mathop{{{\mathbf{A}}_{1}}}}\,=A,\,\,\overset{\to }{\mathop{{{\mathbf{A}}_{2}}}}\,=-A\] \[\therefore \] \[\Delta \overset{\to }{\mathop{\mathbf{A}}}\,=-A-A=-2\overset{\to }{\mathop{\mathbf{A}}}\,\] Also, \[|\overset{\to }{\mathop{\mathbf{A}}}\,|=|-\overset{\to }{\mathop{\mathbf{A}}}\,|\] \[\therefore \] \[\Delta |\overset{\to }{\mathop{\mathbf{A}}}\,|=0\]
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