u=4i-j, v=4i+j, w=i+3j.

Question

Find the specified scalar: u(v+w)

Answer 1

Since the problem states "find the specified scalar", then it must be the dot product since the cross product yields a vector not a scalar:

 

     u·(v+w) = u·(4i+j + i+3j) = u·(5i + 4j) = (4i - j)·(5i + 4j)

 

Now the rule for the dot product is multiply the i terms, then multiply the j terms, then add:

 

     (4i - j)·(5i + 4j) = 4·5 + (-1)·4 = 20 - 4 = 16