**Find a unit vector that is orthogonal to both i + j and i + k.**

**Answer:**

let us assume a vector x = ai+bj+ck is a unit vector as well as orthogonal to i+j and i+k

so then properties of unit vector

a^{2}+b^{2}+c^{2}= 1 eq.1

and orthogonal to i+j and i+k then dot product must be equal to 0

(ai+bj+ck).(i+j) =0 ; a+b =0 : b = -a

(ai+bj+ck).(i+k)=0 ; a+c=0 : c = -a

now putting these values of a and c in eq.1

then a^{2}+(-a)^{2}+(-a)^{2} =1

a=+1/sqrt{3} or-1/sqrt{3}

so the resulting vectors are

x=1/sqrt{3}-1/sqrt{3}-1/sqrt{3}

and y= -1/sqrt{3}+1/sqrt{3}+1/sqrt{3}