Given that a x b is perpendicular to each one of the vectors a and b, determine a unit vector which is perpendicular to each one of the vectors a = 2i - j + k and b = 3i + 4j - k.
Calculate also the sine of the angle, between a and b.

To find the sine of the angle between the vectors use the cross product.







So, we have:





Please, check the calculations.

Look here for how to calculate the cross product if you didn't know: Cross Product -- from Wolfram MathWorld

galactus already gave you the cross product: -3i+5j+11k
Now you just need to find the normal
The normal of a vector is the vector with each term divided by the magnitude of the vector.
For example, the normal of 3i+4j is 3/5i+4/5j since the magnitude of 3i+4j is 5

(note, I didn't double check any of galactus' work so make sure to do that yourself!)