ok so if i do something like this on matlab:
v = [3,3,3];
k = [0,0,1];
w = cross(k,v);
d = cross(w,v);
d = d/norm(d)
d =
0.4082 0.4082 -0.8165
i should get a unit vector d on point v that points towards point k ? will this work for arbitrary values of v & k ?
Is there a way to solve the vectors using just a point on the axis and a unit vector towards the direction we want indicated ? I found something similar on the web, will this work?
"Let r2u be a unit vector from the center of the Earth's surface to
point 2. This unit vector is just a vector...
I assume this is rather elementary so I'll be brief.
I have a point in an xyz coordinate system, this point is assumed to lie on the surface of a sphere with radius R. Suppose I know the coordinates of this point, how would I go about solving for the unitvectors pointing "due north", "due...
How does one form a laurent series about the point z0 = 2i
for the function:
4cos(z*pi) / (z-z0).
Could one take advantage of the power series
1 / (z - z0)
1 / (z - 2i)
SUMMATION q^n
= SUMMATION (2i)^n
= 1 + 2i -4 -8i . . . . .
and somehow integrate the rest of the...
If i have a closed pathintegral of the form:
(sin(z)+3cos(z) + 3e^z)/((z-(pi/2)^2)
How is cauchys integral formula applicable? If I split the integral into partial fractions won't i still get A/(z-pi/2) + B/(z-pi/2)^2, the B part of which won't be applicable to cauchys formula since the...
Hi I have a parametrisation of the unit circle
z = cos(t) + isin(t) = e^(it)
now i guess that the conjugate of that is the same but with a negative coefficient on the imaginary part, namely:
conj z = cos(t) - isin(t)
How does that extend to the e^(it) form? is the following true:
cos(t) -...
Homework Statement
Find the volume of the largest rectangular box with faces parallel to the coordinate planes that can be inscribed inside the ellipsoid :
(x^2/a^2)+(y^2/b^2)+(z^2/c^2) = 1
Homework Equations
Volume of a rectangular box = x * y * z
critical point formula.
The...
Homework Statement
find the largest volume of a rectangular box that satisfies the following condition
the sum of the height and horizontal perimeter does not exceed L
Homework Equations
critical point formula:
system of equations must satisfy the following at critical values of x & y
fx...
Homework Statement
infinity
SIGMA sqrt(n) / ((n^2)(ln(n))
n = 2
Homework Equations
The Attempt at a Solution
Could i beat this into a p-series perhaps?
Homework Statement
Find the closed form value for
n
SIGMA e^(i/n)
i= 0
Homework Equations
?
The Attempt at a Solution
summation expands to
1 + e^(1/n) + e^(2/n) - - - - - e^1
To be honest i have no clue how to go about these kinds of problems so a general help would...