All Questions
19
questions
0
votes
1
answer
41
views
Prove that the addition of two unit vectors bisect the angle between the vectors themselves
Here is a picture for clarity:
So here is what I attempted:
$a \dot{} b = |a||b|\cos(\theta)$
$a \dot{} (\hat{a}+\hat{b})$ $= |a||\hat{a}+\hat{b}|\cos(\gamma)$
$a \dot{}$ $(\frac{a}{|a|} + \frac{b}...
- 1,190
1
vote
1
answer
70
views
Problem with solving simultaneous equations
In part v of part a of the question, they asked me to find the coordinates of point P. I know that:
Also note that part v of question relates back to part iv(for context)
$|OP| = |AP| = |BP| = 5\sqrt{...
- 1,190
1
vote
1
answer
259
views
What does being proportional mean?
Question:
Two concurrent forces act along the sides CA and CB of a triangle. Their magnitudes are proportional to $\cos (A)$ and $\cos (B)$ respectively. Prove that their resultant is proportional to $...
- 3,186
1
vote
1
answer
86
views
Versors (Vectors) and Trigonometry
I recently remebered, when I asked my physics high school teacher if unit vectors are somehow related to sine and cosines (or trigonometry in general). She replied to me that I was pretty lost and ...
- 775
1
vote
2
answers
337
views
How to find the tension in a wire connecting three spheres?.
The problem is as follows:
The diagram from below shows three spheres identical in shape and weigh $6\,N$. The system is at static equilibrium. Find the tension in Newtons ($\,N$) of the wire ...
- 4,185
0
votes
2
answers
2k
views
How to find the tilted angle from a set of hanging masses between two pulleys?
The problem is as follows:
The figure from below shows three masses tied to a central one which
is hanging with respect of a floor. Find the angle so that the system
remains in static ...
- 4,185
0
votes
1
answer
476
views
Directional Vector Word Problem
So here's the problem: Suppose a bird is flying NE at 5m/s into a headwind blowing at 2m/s 30° SE. Find the NE direction in which the bird was flying and it's resulting speed in the east direction.
...
- 31
0
votes
1
answer
53
views
Precal Vector Dot Product
Find the dot product $a • b$ and the angle between the two vectors in each set.
$a=\binom{3}{-1}$, $b= \binom{-1}{2}$
(note: the vector notation above is not exactly a vector notation, but it is ...
- 4,581
0
votes
1
answer
159
views
How to find two orthogonal vectors $a$ and $b$ such that $a$ is the projection of vector U on V and $a+b=U$
Given that U=<2,6> and V=<9,2> find two orthogonal vectors $a$ and $b$ such that $a$ is the projection of vector U on V and $a+b=U$
I first wanted to know how to even do this problem and ...
- 2,685
1
vote
1
answer
73
views
Vectors $a$ and $b$ each have length $6$ and form an angle of $45°$ . Let $u = a + 2b$ and $v = 2a - b$. What is the angle formed by $u$ and $v$?
Suppose vectors $a$ and $b$ each have length $6$ and form an angle of $45°$ . Let $u = a + 2b$ and $v = 2a - b$. What is the angle formed by $u$ and $v$ ?
I've drawn vector a and b on a coordinate ...
- 2,685
1
vote
1
answer
374
views
Figure Out Direction of Plane (Heading) — Slightly Complicated?
Bearing = Measured from Due North ($310^\circ$ bearing = $140^\circ$)
We are given the following — a plane departs from airport LAX to SFO at an air speed of 750 km/hr at 12:00 AM, with airport SFO ...
- 177
1
vote
1
answer
49
views
Precision of Manual Vector Addition
I learned the fundamentals of vectors and basic (e.g. addition, dot product) vector operations in a Trigonometry course, and they're being reintroduced in the Physics I course I just began.
My ...
- 709
0
votes
1
answer
2k
views
Airplane ground speed and direction, given airspeed and wind
An airplane heads northeast at an airspeed of 900 km/hr, but there is a wind blowing from the west at 60 km/hr. In what direction does the plane end up flying? (angle). What is its speed relative to ...
- 43
6
votes
3
answers
88
views
Line for set of three-dimensional vectors
If there is a set for 3D vectors $v$ where
$ v \times \begin{pmatrix} -1 \\ 1 \\ 4 \end{pmatrix} = \begin{pmatrix} 5 \\ -27 \\ 8 \end{pmatrix}$
is a line, what is this line's equation?
I'm not sure ...
- 1,725
2
votes
2
answers
314
views
Intersection between two three-dimensional planes
The intersection of the planes defined by
$x \bullet \begin{pmatrix} 8 \\ 1 \\ -12 \end{pmatrix} = 35$
and
$x \bullet \begin{pmatrix} 6 \\ 7 \\ -9 \end{pmatrix} = 70$
is a line. Find an equation of ...
- 1,725