# Maths Homework

1. Mar 30, 2009

### arsalan_y

1. The problem statement, all variables and given/known data
Im stuck on a few questions i cant seem to find the methods in my notes. the questions are:

1.The points P, Q, and R have coordinates P = (1, 0,−1),Q = (1,−2, 5) and R = (0,−3, 2).
State which pair of points are closest to each other.
2.A 2-dimensional force of 5[units] in the direction of the line y = 3x (upwards) acts through the
point P = (−1,−2). Find the moment of the force about the origin.
3.Find the solution to the differential equation below, corresponding to y(0) = 1/3
dy/dx= 2(x − 1)2 + x cos (−x2)

2. Relevant equations

i dont know where to start for any of them

3. The attempt at a solution

2. Mar 30, 2009

### foxjwill

1) do you know the formula for distance between two points?

2) Do you know the formula for the "moment of force" (i.e. torque) about the origin?

3) I'm assuming you mean

$$\frac{dy}{dx}=2(x-1)^2 + x\cos(-x^2).$$​

If this is the case, then the first (and most important) thing to notice is whether the right-hand side (RHS) depends on just y, both x and y, or just x. Which one is it? How would this help you solve it?

3. Mar 30, 2009

### arsalan_y

is the equation
d = square root of [(x2-x1)2 + (y2-y1)2 + (z2-z1)2]
for the 1st question?

4. Mar 30, 2009

yes, it is

5. Apr 1, 2009

### arsalan_y

i dont know the equation for the 2nd question

6. Apr 1, 2009

### foxjwill

Let $$\vec{F}$$ be a force with magnitude F acting at a point P, and let $$\vec{l}$$ be the displacement vector (with magnitude $$l$$) drawn from the origin to P. Let $$F_\bot$$ be the component of $$\vec{F}$$ perpendicular to $$\vec{l}$$. The moment of force about the origin is a vector $$\vec{\tau}$$ with magnitude

$$\tau = lF_\bot$$

and direction determined by the right-hand rule with $$\vec{l}$$ as "vector one" and $$\vec{F}$$ as vector two.