Byron S. answered • 10/20/14

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.

tutor

Let's see.. w·w is 0

^{2}+ (-2)^{2}+ (-1)^{2}= 55u = <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

Byron S.

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

Byron S.

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