Inactive Tutor answered • 10/20/14
Tutor
New to Wyzant
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.
Inactive Tutor
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!
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10/20/14
Inactive Tutor
Sorry, sign errors, that should be 240, not 80!
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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!
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10/20/14
Inactive Tutor
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!
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10/20/14
Dalia S.
10/20/14