2
votes
2answers
99 views

check if point is on a plane (using Heron formula ?)

Is this true that if any of parameters a, b, c, d is equal to sum of three others then 4 points are on same plane? I am given 4 points in 3 dimensional space. Is this correct to state that all 4 ...
1
vote
0answers
139 views

Computing Euler Angles from Direction Cosines Vector

My problem simply as the following: Suppose we measured the orientation of a plane object with respect to a reference fame. (where the reference frame parallel to plane frame). The unit normal vector ...
0
votes
1answer
2k views

Equation of a line passing through a given point, perpendicular with a vector

Find the line that goes through A(1,0,2) and is perpendicular to r = (-2,3,4) + s (1,1,2) I did a bunch of work, but I don't know if any of it is right. I erased most of it, but this is what I came ...
5
votes
0answers
179 views

Are there eigenvectors, eigenvalues, and characteristic functions for non-linear vector fields?

An eigenvector is a vector in the preimage of the transformation whose direction is not changed when the transformation is applied. It seems like the concept of eigenvectors and eigenvalues would ...
5
votes
1answer
168 views

Cross Product Intuition

I know the cross product between a vector $a$ and a vector $b$ is just a vector whose magnitude is the product of magnitude of $b$ times the magnitude of the perpendicular component of $a$ in relation ...
0
votes
1answer
89 views

Lines which intersect the postive half axis of x

We have to find out which lines intersect the postive half axis of x. According to this formula we can determine if the angle between two points(A[x1,y1] and B[x2,y2]) of the line (angle A0B where 0 ...
6
votes
7answers
876 views

Detect when a point belongs to a bounding box with distances

I have a box with known bounding coordinates (latitudes and longitudes): latN, latS, lonW, lonE. I have a mystery point P with ...
1
vote
1answer
1k views

Parametric equation for a line which lies on a plane

Struggling to begin answering the following question: Let $L$ be the line given by $x = 3-t, y= 2+t, z = -4+2t$. $L$ intersects the plane $3x-2y+z=1$ at the point $P = (3,2,-4)$. Find parametric ...
3
votes
1answer
290 views

Maximum cosine for angle between 2 vectors when 1 vector is partially unknown

assuming I have two vectors $A$ and $B$, where $A$ is completely known and from $B$ I know only that the first k components are 0. What is the maximum possible cosine value for the angle between the ...
0
votes
1answer
18 views

What is $a$ in the formula for the distance of point to plane formula: $h=\frac{|(a-p) \cdot n|}{|n|}$?

What does $a$ stand for in the following formula for the distance of a point to a plane? $$h = |PF| = \frac{|d - p \cdot n|}{|n|} = \frac{|(a-p)\cdot n|}{|n|} .$$
1
vote
1answer
65 views

If $\|\mathbf{OA}+k\mathbf{OB} \|=1$, prove that $\text{Area}(OACB) \leq \| \mathbf{OB} \|$

OACB is a parallelogram. In other words if $\left \|\mathbf{a}+k\mathbf{b} \right \|=1$ ($k\in\mathbb{R}$), prove that $$\|\mathbf{a}\| \cdot \|\mathbf{b} \| \cdot \sin \theta \leq \|\mathbf{b} \| $$ ...