Question

Multiplying or dividing vectors by scalars results in a. vectors. b. scalars. c. vectors if multiplied or scalars if divided. d. scalars if multiplied or vectors if divided.

Answer 1

Let A = i+j+k be a vector and B = 3 be any scalar, 
Multiplying A and B, 
AB = (i+j+k)3 = 3i+3j+3k 

Which is a new vector whose direction is same as the old but it's 3 times greater in length  than the old vector(i+j+k).

Now, dividing A and B,
A/B = (i+j+k)/3 = $\frac{1}{3}i + \frac{1}{3}j + \frac{1}{3}k$

Which is again a new vector whose direction is same as the old but now it's 1/3 times small in length than the old vector. 

Direction is same because we multiplied by positive scalar. If we multiply A by suppose -1, -4, -1000000 or any negative number, it's direction will reverse. 

Thus, if we multiply a vector with scalar, it's length increases. If we divide, it shrinks. 

Answer 2

Always vectors. Remeber that multiplication and division are the same thing. When you want to divide by 2, you are really just multiplying by (1/2). Also remember that multiplying a vector by a scalar does not change the vector into a scalar. It keeps it a vector.