Can I know if my answer is correct please?

Question

Two vectors a and b are given. a = <2,5,3> and b = <4,-2,-1> (a) Find a vector perpendicular to both a and b. My answer is <1,14,-24> (b) Find a unit vector perpendicular to both a and b. My answer is <1/sqrt773, 14/sqrt773, -24/sqrt773>

Answer 1

Yes it is correct as you can directly check

$$(2,5,3)(1,14,-24)=2+70-72=0$$

$$(4,-2,-1)(1,14,-24)=4-28+24=0$$

and also the coefficient to normalize is correct indeed

$$1^2+14^2+24^2=773$$