All Questions
11
questions
2
votes
0
answers
210
views
Let $|\vec a|=|\vec b|=2$ and $|\vec c|=1$.Find the difference between maximum and minimum possible values of $|\vec a+\vec b|$
Let $|\vec a|=|\vec b|=2$ and $|\vec c|=1$. Also $(\vec a-\vec c)\cdot(\vec b-\vec c)=0$.
Find the difference between maximum and minimum possible values of $|\vec a+\vec b|$
My Attempt
$|\vec a+\vec ...
- 9,599
4
votes
2
answers
342
views
If $\vec a,\vec b,\vec c$ be three vectors such that $|\vec a|=1,|\vec b|=2,|\vec c|=4$ and then find the value of $|2\vec a+3\vec b+4\vec c|$
If $\vec a,\vec b,\vec c$ be three vectors such that
$\vert \vec a\vert =1,\vert \vec b\vert =2,\vert \vec c\vert=4$
and
$\vec a \cdot \vec b+\vec b \cdot \vec c+\vec c \cdot\vec a=-10$
then find the ...
- 9,599
0
votes
2
answers
61
views
Vectors and Planes with parametric equations
Any help would be appreciated!
Find a parametric equation of a line $L$ that is obtained as the intersection of the planes $P$ and $Q$ with scalar equations $$P: x+2y+3z=4$$ and $$Q: x-3y+z=1$$
...
- 475
2
votes
3
answers
271
views
How to find vector from point along line lying on a direction vector?
Sorry if the title's confusing. I've been trying to solve this problem with no avail:
Let $V = (0,3,2)$ and $A = (-1,0,1).$ Let $P$ be the point on the line passing through $A$ with direction vector $...
- 45
1
vote
1
answer
81
views
Finding a Vector Perpendicular to Two Other Vectors w/o Cross Products
I need to find a vector that is perpendicular to the vectors $[2, 3, 2]$ and $[4, 9, 5]$. I have not been taught the method with cross-products using matrices so I cannot use that method while solving ...
- 808
1
vote
2
answers
734
views
When getting the cross product of two vectors, is the i value initially positive or negative? [ERROR ON MY END]
[upon further discussion it appears this was just a sign error when performing operations with the matrix (comments in first answer)]
given
$$
\vec{u} = \frac{1}{2} i -1j+\frac{2} {3} k ,\
\...
- 113
0
votes
1
answer
13k
views
Finding the length of a 3-dimensional vector
I am struggling with a Linear Algebra problem that involves finding the length of a 3-dimensional vector $\mathbf r$, as shown in the picture I sketched:
I do not have the coordinates of the points ...
user423442
2
votes
0
answers
156
views
Vector equation of line containing point and perpendicular to plane [duplicate]
How would one find the vector equation of the line that contains the point (x0, y0, z0) and is perpendicular to the plane Ax + By + Cz = D?
- 321
2
votes
2
answers
93
views
What does the homogeneous system of equations represent under certain conditions?
Consider the following linear equations
$ax+by+cz=0,bx+cy+az=0,cx+ay+bz=0$
1) $a+b+c \neq o$ and $a^2+b^2+c^2=ab+bc+ca$
2) $a+b+c \neq o$ and $a^2+b^2+c^2 \neq ab+bc+ca$
3) $a+b+c =...
user220382
0
votes
4
answers
9k
views
How to find perpendicular vectors in 3D
Find all values of a such that the vector $q = \langle 2, a, –2\rangle$ is perpendicular to the vector
$p = \langle –3, a, 5 \rangle$.
- 95
1
vote
1
answer
58
views
Question about 3D vectors and their line equations.
Let
${a} = \begin{pmatrix} 5 \\ -3 \\ -4 \end{pmatrix} \quad \text{and} \quad {b} = \begin{pmatrix} -11 \\ 1 \\ 28 \end{pmatrix}.$
There exist vectors ${p}$ and ${d}$ such that the line containing ${...
user233734