SOLUTION: 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⟩
Algebra.Com
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(13241) (Show Source): You can put this solution on YOUR website!
The dot product is a number, not a vector.
(3u)*v = 3<5,-4> * <7,8> = <15,-12> * <7,8> = 15*7-12*8 = 105-96 = 9
Answer by math_tutor2020(3827) (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).
RELATED QUESTIONS
Find 3U + 2V given the vectors U = -i + 4j and V = 2i... (answered by Fombitz)
Use the vectors u = <-3, 4> and v = <2, 1>.
3u • v =... (answered by Alan3354)
Use the vectors u = <2, 2>, v = <-3, 4> and w = <1, -2> to find the indicated quantity.
(answered by math_helper,rothauserc)
-3/2 + 1/3u = -4/5... (answered by tommyt3rd)
Let u and v be the vectors of length 3 and 5, respectively. Suppose u . v = 8. Find... (answered by robertb)
Here is my problem, concerning vectors and norms(?)
I have the following information:
u (answered by jim_thompson5910)
Given u=(5,-3) and v=(2,9) find the dot product of 2u times v. Thanks (answered by Fombitz)
Has this problem been resolved correctly?
Find the angle between two vectors u=3i+4j... (answered by math_tutor2020)
1. The magnitude and direction of vectors u and v are given. Find vector w's polar... (answered by richard1234)