Question

find the unit vecter in the direction of a=i+j+k

Answer 1

To do this task we need to normalize the given vector. At first, let's find its magnitude:
r=sqrt(1+1+1)=sqrt(3)
Now we divide each vector in the sum by this obtained number:
a0=a/sqrt(3)=(i+j+k)/sqrt(3)=i/sqrt(3)+j/sqrt(3)+k/sqrt(3)
What we now have is a vector a0 which has the same direction as initial one (v=because dividing vector by positive number doesn't change its direction). Also obtained vector a0 has unit length:
length(a0)=sqrt(1/3+1/3+1/3)=1
So the task is complete

Answer: (i+j+k)/sqrt(3)