“Determine wether u and v are orthogonal, parallel or neither, where: u = <1,2,3> and v = <4/3,8/3,4>.
I am thinking they’re parallel.”
The Dot Product
u • v = (1)(4/3) + (2)(8/3) + (3)(4), and
u • v = √(1+4+9)√(16/9 + 64/9 + 16) cos(θ),
where θ is the angle between the vectors.
cos(θ) = ((1)(4/3) + (2)(8/3) + (3)(4))
/(√(1+4+9)√(16/9 + 64/9 + 16))
= (4/3 16/3  36/3)/√((14)(80/9 + 144/9))
= (56/3)/√((14)(80/9 + 144/9))
= 56/√((14)(80 + 144))
= 56/56
= 1
θ = 180° so the vectors are parallel.
==
“1)Find the vector z = 2u + (1/2)v  3w,
given u = <1,3,2>, v = <6,2,2> and w = <5,0,5>.
So i am thinking that i have to first find the internal and terminal point to find the component”
u = <1,3,2>
v = <6,2,2>
w = <5,0,5>
z = 2u + 1/2v  3w
2u = <2,6,4>
(1/2)v = <3,1,1>
3w = <15,0,15>
z = <(2+315,61+0,41+15>
z = <10,7,10>
3/12/2014

Steve S.