If c is a unit vector perpendicular to the vectors a and b, write anot

1.	If c is a unit vector perpendicular to the vectors a and b, write another unit vector perpendicular to a and b.
Answer» We know that cross product of two vectors gives us a vector which is perpendicular to both the vectors. And keeping in mind that is a Unit vector we get the equation – \(\cfrac{\vec a\times\vec b}{\|\vec a\times\vec b\|}=\vec c\)→(Vector divided its magnitude gives unit vector) \(\cfrac{\vec a\times\vec b}{\|\vec a\times\vec b\|}=-\vec c\) \(\therefore-\vec c\) is perpendicular to \(\vec a\) and \(\vec b\). Alternative Solution – Since \(\vec c\) is perpendicular to \(\vec a\) and \(\vec b\), any unit vector parallel/anti-parallel to \(\vec c\) will be perpendicular to \(\vec a\) and \(\vec b\).

If c is a unit vector perpendicular to the vectors a and b, write another unit vector perpendicular to a and b.

Answer»

We know that cross product of two vectors gives us a vector which is perpendicular to both the vectors. And keeping in mind that is a Unit vector we get the equation –

\(\cfrac{\vec a\times\vec b}{|\vec a\times\vec b|}=\vec c\)→(Vector divided its magnitude gives unit vector)

\(\cfrac{\vec a\times\vec b}{|\vec a\times\vec b|}=-\vec c\) \(\therefore-\vec c\) is perpendicular to \(\vec a\) and \(\vec b\).

Alternative Solution – Since \(\vec c\) is perpendicular to \(\vec a\) and \(\vec b\), any unit vector parallel/anti-parallel to \(\vec c\) will be perpendicular to \(\vec a\) and \(\vec b\).

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