The unit vector perpendicular to a and b is

η = (a * b)/|a * b|

Now, a * b = |i     j    k|

                    |2  -1   1|

                    |3   4  -1|

=> a * b = i(1 - 4) - j(-2 - 3) + k(8 + 3)

=> a * b = -3i + 5j + 11k

Now,  |a * b| = √{(-3)² + 5² + (11)² } = √{9 + 25 + 121} = √155

So, η = (-3i + 5j + 11k)/√155

So, the unit vector perpendicular to a and b is (-3i + 5j + 11k)/√155

Again a . b = |a|*|b|*cos θ

=> cos θ = (a . b)/(|a|*|b|)

=> cos θ = {(2i - j + k).(3i + 4j - k)}/[{√{2² + 1² + 1² }*√{3² + 4² + (-1)² }]

=> cos θ = (6 - 4 - 1)/[{√{4 + 1 + 1 }*√{9 + 16 + 1}]

=> cos θ = 1/{√6 *√26}

=> cos θ = 1/√{6*26}

=> cos θ = 1/√156

Now sin θ = √(1 - cos² θ)                {since sin² θ + cos² θ = 1}

=> sin θ = √{1 - (1/√156)² }

=> sin θ = √{1 - 1/156 }

=> sin θ = √{(156 - 1)/156 }

=> sin θ = √(155/156)