If vectors vector a1=x hat i- hat j+hat k and vector a2=hat i+y hat j+z hat k are collinear, then apossible unit vector parallel to the vector

Question

If vectors \(\vec a_1=x\hat i-\hat j+\hat k\) and \(\vec a_2=\hat i+y\hat j+z\hat k\) are collinear, then a possible unit vector parallel to the vector \(x\hat i+y\hat j+z\hat k\) is 

Answer 1

Correct option is (4) \(\frac{1}{\sqrt 3}(\hat i-\hat j+\hat k)\) 

\(\vec a_1\) and \(\vec a_2\) are collinear 

so x/1 =-1/y = 1/z

unit vector in direction of

\(x\hat i+y\hat j+z\hat k\) \(=\pm{1}{\sqrt3}(\hat i-\hat j+\hat k)\)