SOLUTION: Given u = (2, 4, −3), v = (3, −1, 7), and i,j, k being the standard basis vector, find and provide solutions: a. v − u + 3k b. u.v c. u*v Note: u.v is dot product an

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Question 1163719: Given u = (2, 4, −3), v = (3, −1, 7), and i,j, k being the standard basis vector, find and provide solutions:
a. v − u + 3k
b. u.v
c. u*v
Note: u.v is dot product and u*v is cross product.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Given u = (2, 4, −3), v = (3, −1, 7), and i,j, k being the standard basis vector, find and provide solutions:
=-===============
I'll use 2 different vectors to show how to do it.
u = (-2,3,5), v = (3,1,-4)
a. v − u + 3k

v = (3,1,-4)
u = (-2,3,5)
------------------------ Subtract
--->(5,-2,-9)
-------------------------
Add 3k
---> (5,-2,-6)

========
b. u.v
u.v = 3*-2 + 1*3 + -4*5 ---- Add them
=================
c. u*v
| i   j   k|
|-2   3   5|
| 3   1  -4|

i*(3*-4 - 1*5) - j*(-2*-4 - 3*5) + k*(-2*1 - 3*3)
= -17i + 7j - 11k


Note: u.v is dot product and u*v is cross product.
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