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If $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=0$ and $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}=\overrightarrow{0}$ then which one of the following is
correct ?
Options:
correct ?
Solution:
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Verified Answer
The correct answer is:
$\overrightarrow{\mathrm{a}}=\overrightarrow{0}$ or $\overrightarrow{\mathrm{b}}=\overrightarrow{0}$
$\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=0 \Rightarrow \overrightarrow{\mathrm{a}} \perp \overrightarrow{\mathrm{b}}$
$\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}=0 \Rightarrow \overrightarrow{\mathrm{a}} \| \overrightarrow{\mathrm{b}}$
(ii) it is clear that $\overrightarrow{\mathrm{a}}=0$ or $\overrightarrow{\mathrm{b}}=0$ From (i) and
$\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}=0 \Rightarrow \overrightarrow{\mathrm{a}} \| \overrightarrow{\mathrm{b}}$
(ii) it is clear that $\overrightarrow{\mathrm{a}}=0$ or $\overrightarrow{\mathrm{b}}=0$ From (i) and
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