If a=i-j and b=i+k then a unit vector coplanar with a and b and perpendicular to a is

Dear pallavi

you can take any vector in plane of two given vector

r =xa +yb

 =x(i-j) +y (i+k)

 =i(x+y) -xj +yk

if it is perpendicular to a then

 r.a=o

{i(x+y) -xj +yk}.(i-j)=0

2x+y=0

so r will become r= -x[i+j +2k]

 if it is a unit vecttor then ( x² + x² +4x²)^1/2=1

                                       x= ±1/√6

so r= ±1/√6[i +j+2k]

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