The basics Flashcards
to connect variouse ideas from ch.13 to ch.12, should include practice problems.
1
Q
V!+W!
A
W!+V!
2
Q
a(bW!)
A
(ab)W!
3
Q
(V!+W!)+U!
A
V!+(W!+U!)
4
Q
(a+b)V!
A
aV!+bV!
5
Q
1V!
A
V!
6
Q
0V!
A
0!
7
Q
V!+0!
A
V!
8
Q
W!+(-1)U!
A
W!-U!
9
Q
V! * W!
A
W! * V!
10
Q
(aV!)W!=V!(aW!)
A
a(V!*W!)
11
Q
(V!+W!)U!=V!U! + W!*U!
A
IIV!II^2=V!*V!
12
Q
If V! and W! are parallel
A
V! x W! = 0
12
Q
U! x (V! + W!)=
A
U! x V! + U! x W!
12
Q
V! x W!
A
-W! x V!
13
Q
(aV!) x (W!) = V! x (aW!)
A
a(V! x W!)
13
Q
area of a parallelogram
A
IIV! x W!II
14
Q
area of a triangle
A
1/2 IIV! * W!II
15
Q
arithmetic equation dot product
A
V!xW!x+V!yW!y+V!zW!z
16
Q
geometric equation dot product
A
IIV!II IIW!II cos(theta)
17
Q
normal vector
A
is perpendicular to plane
18
Q
normal vector plane equation
A
PoP! * n! = a(x-xo)+b(y-yo)+c(z-z0)
19
Q
unit vector
A
V!/IIV!II
20
Q
unit vector over a certain distance
A
dV!/IIV!II
21
Q
geometric equation for cross product magnitude
A
IIV! x W!II = IIW!II IIV!II sin(theta)
22
geometric equation for cross product
V! x W! = IIV!II IIW!II sin(theta) n!
23
matrix for agebraic cross product
V! x W! = (V2W3 - V3W2)i! - (V1W3-V3W1)j! + (V1W2-V2W1)K!
24
