a) [-3,2,5] + t[-4,4,1]

b) [1,-2,4] + t[-4,4,1]

c) Both of the above

d) None of the above

a) |v||w| cos(theta) where theta is the angle between them

b) |v||w| sin(theta)

c) v1w1+v2w2+v3w3

d) all of the above are true

e) 2 of a), b) c) are true

a) If they are parametrized by time then it is the same calculation

b) They are always equal

c) For tangent take the component derivatives with respect to the parameter in the parametrization, for velocity take the component derivatives with respect to time

d) all of the above are true

e) 2 of a), b) c) are true