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Question

The unit vector perpendicular to i^-j^and coplanar withi^+2j^andi^+3j^ is?


A

2i^-5j^59

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B

2i^+5j^

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C

i^+j^2

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D

i^+j^

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Solution

The correct option is C

i^+j^2


Explanation for correct option

Let the unit vector be a^=xi^+yj^

As per the given condition, a is perpendicular to vector i^-j^

Therefore,

a^.(i^-j^)=0(xi^+yj^).(i^-j^)=0x-y=0x=y

So, we can write,

a^=xi^+xj^|a^|=x2+x2=x2

Therefore, the unit vector a^=x(i^+j^)x2=i^+j^2

Hence, the correct option is OptionC


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