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Home Q & A Board Science-Related Homework Help Physics
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final_ace final_ace
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11 years ago
How do you find the dot product v times w and the angle between v and w?

v=-2i+j+3k w=i+2j+4k
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#1
11 years ago
For  v.w, multiply the corresponding components of each vector, then add them together.

(-2*1)+(1*2)+(3*4) = 12

For the angle between v and w:

v.w = |v||w| Cos theta [where theta is the angle between v and w]

Cos theta |v|w| = v.w

Cos theta = (v.w)/(|v||w|)

|v| = ?(-2)^2+(1)^2+(3)^2 = ?14
|w| = ?(1)^2+(2)^2+(4)^2 = ?21

Cos theta = 12/(?14 *?21)

theta = Cos^-1 (12/(?14 *?21) )

theta = 45.58?

         = 45.6?

Hope this helps.
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