Hello! Im writing a linear Algebra test in January and im currently practicing. But my problem is, that its hard to verify my
results so id thought i could post here. Please tell me if its not appropiate. Besides that, im still not ablle to solve all
questions asked. Many thanks in advance
I have a Parallelogram given by the Points A,B,C,D created in counter-clockwise direction. The middle intersection of the
Lines AC and BD is the point M.
I have the following Points given:
Question 1: What is the length of AB ?
i have: AB = [4-3;0+2;1-3] = [1;2;-2]
|AB| = square root of 1+4+4 = 3 which is my lenght
QUestion 2: Parametric euqation of the Plane ABM and which parameters result in the Position vector of C ?
my attempt: E(c,k) = [3;-2;3] + c[4-3;0+2;1-3] + k[4-6;0-3;1-7] = [3;-2;3] + [c;2c;-2c]+[-2k;-3k;-6k]
which would describe my Plane ABM in parametric form
Now position vector of C with the parameters of c,k in the Plane equation.
My thinking: the length of AC is twice as long as the length AM. So i came to the conclusion my parameters should be
c = 0 since i dont need to go in the direction of point B
and d = 2 since its twice as long. Really not sure how to solve that more delicate
Question 3: Find the vector v perpendicular to the Plane ABM, such that it is pointing downwards
I think i need something like a Normalvector found by a crossproduct. But im confused since i thought i needed only 2 vectors
Question 4: Find the cosine of the angle between the lines AB and AC at the point A
cos(phi) = [ (v1 * v2) / (|v1| x |v2|) ]
v1 = AB = [3;-2;3] +c [4;0;1]
v2 = AC = A2M
not sure about that last one