Byron S. answered • 10/20/14
Tutor
5.0
(44)
Math and Science Tutor with an Engineering Background
The dot product of two vectors is the sum of the product of each pair of corresponding vectors, and the result is a scalar value, not a vector
u = <4, -4, 4>
v = <4, 2, -4>
w = <0, -2, -1>
u·v = 4*4 + (-4)*2 + 4*(-4) = 16 - 8 - 16 = -8.
(u·v)u = -8u
Just multiply each component of u by -8.
[(u·v)u]·u
Find the dot product of the last answer times the original u vector.
u·v+v·w
u·v = -8, from above
v·w you can find the same way, with vectors v and w instead of u and v
Once you find this, just add the two values together.
I hope this helps. If you have further questions, please comment.
Byron S.
Let's see.. w·w is 02 + (-2)2 + (-1)2 = 5
5u = <20, -20, 20>
(5u)·u = 20*4 + -20*-4 + 20*4 = 80
Don't forget that a dot product is the sum of the products!
Report
10/20/14
Byron S.
Sorry, sign errors, that should be 240, not 80!
Report
10/20/14
Dalia S.
ohhh ok, my mistake was that i forgot to add the dot products at the end, thank you for your help!
Report
10/20/14
Byron S.
Your middle term should also be (-20)*(-4) = +80, not -80. (I did the same thing while multiplying in my head.) Otherwise, you're in good shape!
Report
10/20/14
Dalia S.
10/20/14