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Vector or Cross Product — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVector or Cross Product2 Marks
Question
If $\vec{\text{c}}$ is a unit vector perpendicular to the vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ write another unit vector perpendicular to $\vec{\text{a}}$ and $\vec{\text{b}}.$
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Answer

$\vec{\text{c}}$ is a unit vector perpendicular to both $\vec{\text{a}}$ and $\vec{\text{b}}.$
$\Rightarrow\vec{\text{c}}=\frac{\vec{\text{a}}\times\vec{\text{b}}}{\big|\vec{\text{a}}\times\vec{\text{b}}\big|}$
$\Rightarrow-\vec{\text{c}}=\frac{\vec{\text{b}}\times\vec{\text{a}}}{\big|\vec{\text{a}}\times\vec{\text{b}}\big|}$
Therefore, $-\vec{\text{c}}$ is perpendicular to $\vec{\text{b}}$ and $\vec{\text{a}}.$
Thus, $-\vec{\text{c}}$ is another unit vector perpendicular to $\vec{\text{a}}$ and $\vec{\text{b}}.$

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