A) \[\overset{\to }{\mathop{\mathbf{a}}}\,\bot \overset{\to }{\mathop{\mathbf{b}}}\,\]
B) \[\overset{\to }{\mathop{\mathbf{a}}}\,||\overset{\to }{\mathop{\mathbf{b}}}\,\]
C) \[\overset{\to }{\mathop{\mathbf{a}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]and\[\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]
D) \[\overset{\to }{\mathop{\mathbf{a}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]and\[\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]
Correct Answer: D
Solution :
Since, \[\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\] \[\therefore \]\[\overset{\to }{\mathop{\mathbf{a}}}\,\]is perpendicular to\[\overset{\to }{\mathop{\mathbf{b}}}\,\] And \[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\] \[\therefore \]\[\overset{\to }{\mathop{\mathbf{a}}}\,\]is parallel to\[\overset{\to }{\mathop{\mathbf{b}}}\,\]. Which is possible only, if \[\overset{\to }{\mathop{\mathbf{a}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]or\[\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]
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