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Question

Given the two vectors i-j and i+2j, the unit vector coplanar with the two perpendicular to that first is?


A

(i+k)2

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B

(2i+j)5

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C

±(i+j)2

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D

none of these

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Solution

The correct option is C

±(i+j)2


Explanation for the correct option:

Given, The two vectors are i-jandi+2j

The unit vector is coplanar with the given vectors and lie in XY plane.

a=xi+yj

Now, a is perpendicular to i-j,

soxi+yj.i-j=0

Thus,x-y=0x=ya=xi+xja=x2+y2=x2

Hence , the unit vector a

=aa=xi+jx2=i+j2

Hence option(C) is correct.


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