Posted by Joanie on .
Given vectors u=7i + 3j and v = 4i + 3j, find 5u4v in terms of unit vectors.
I am just beginning the study of vectors and have this problem. Could someone help? Thanks.

PreCalculus 
Reiny,
handle them just like algebraic expressions
u=7i + 3j and v = 4i + 3j
then 5u  4v
= 5(7i+3j)  4(4i+3j)
= 35i + 15j + 16i  12j
= 51i + 3j 
PreCalculus 
Joanie,
Dear Reiny,
Thank you for helping me. Could you check an answer for me?
Use a metric ruler and a protractor to find 2 a (vector)  2 b (vector). Then find the magnitude and amplitude of the resultant.
Vector a is 4 cm and the angle is 60 degrees. Vector b is 1 centimeter long and the angle is 135 degrees.
My answer for magnitude was 4 cm with the angle being 31 degrees. Is this correct? 
PreCalculus 
drwls,
vector a = 4 cos 60 i + 4 sin 60 j
= 2 i + 0.866 j
vector b = 2.828 i + 2.828 j
"i" and "j" indicate the components along the x and y axes. It is a commonly used vector notation
a  b = 0.828 i + 3.694j
magnitude of a  b = 3.785
magnitude of 2 (ab) = 7.571
Your angle is also wrong 
PreCalculus 
Joanie,
Hi drwls
I have just begun the study of vectors. I am given the answer in multiple choiceThe answer you gave me is 7.571. The choices I have are 8cm;41 degrees; 9cm;38degrees;6cm,36degrees, and 4cm,31 degrees.
Your answer is closest to 8 cm. Is that the one I should select? Thanks.