Find the moment of the force about the origi

[arsalan_y]

Homework Statement

Im stuck on a few questions i can't 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)

Homework Equations

i don't know where to start for any of them

The Attempt at a Solution

 

[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?

 

[arsalan_y]

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

 

[foxjwill]

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

yes, it is

 

[arsalan_y]

i don't know the equation for the 2nd question

 

[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.