Question 1202797: Given two vectors u = 5i - 4j and v = 7i + 8j, find dot product
(3u) * v
3u = 3⟨5, 4⟩ = ⟨3(5), 3(4)⟩ = ⟨15, 12⟩
1v = 1⟨7, 8⟩ = ⟨1(7), 1(8)⟩ = ⟨7, 8⟩
(3u ⃗) * v = ⟨15, 12⟩ * ⟨7, 8⟩ = ⟨15 * 7, 12 * 8⟩
(3u ⃗) * v = ⟨105, 96⟩
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13209)   (Show Source):
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Answer: 9
Explanation
Let
u = (a,b)
v = (c,d)
represent two vectors
a,b,c,d are real numbers
The dot product is defined as this operation
u dot v = a*c + b*d
We multiply the corresponding coordinates and add the products.
Before we get to the dot product, let's first compute 3u.
This is the result of tripling the coordinates of vector u.
u = (5,4)
3u = 3*(5,-4)
3u = (3*5,3*(-4))
3u = (15,-12)
Now we can compute the dot product.
(3u) dot v = 15*7 + (-12)*8
(3u) dot v = 105 - 96
(3u) dot v = 9
Extra info:
If the dot product of two vectors is 0, then the vectors are perpendicular (aka orthogonal).
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