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Question

Given that i - j, i + 2j are two vectors. Find a unit vector coplanar with these vectors and perpendicular to the first vector i - j. Find also the unit vector which is perpendicular to the plane of the two given vectors. Do you thus obtain an orthonormal triad ?

A
k
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B
12(i+j);
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C
k
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D
12(ij);
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Solution

The correct options are
A k
B 12(i+j);
Consider the first vector ij
Now a vector co-planar with the two vectors and perpendicular to ij will be of the form r(ij)2 where r is a scalar quantity.
Since we require a unit vector, therefore r=1.
Now the normal vector of the plane containing the two specified vectors will be
(ij)×(i+2j)
=2k+k
=3k
Thus unit vector along the normal of the plane will be
=k.

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