1. ## vector HELP..

A force is given in the vector form,$\displaystyle \hat{F}=3\hat{i}+4\hat{j}+\hat{k}$ passes thru the point P whose coordinates are [1,2,2] in a cartesian coordinate system and $\displaystyle \hat{i},\hat{j},\hat{k}$ are the unit vectors in the x,y and z directions respectively. Q is a point whose coordinates are [4,3,6].

i)Find the vector QP
ii)find the maqnitude the moment of the force $\displaystyle \hat{F}$ about the point Q.
iii)Find the unit vector in the direction of the moment...

If its possible to sketch a diagram too would be great...I just cant understand VECTORS!

2. ## First part

If you think about that $\displaystyle \hat{F}$ act on P to go to T (end point of the vector) like:

$\displaystyle T = \hat{F} + P$

you see that:

$\displaystyle \hat{F} = P - T$

each coordinate is the coefficient of each of the fundamental vectors $\displaystyle \hat{i},\hat{j},\hat{k}$.

In this execise:

$\displaystyle i) \hat{QP} = 3\hat{i}+\hat{j}+4\hat{k}$

I must go now... later i'll complete it.

3. hm...interested to know how to solve this question. any help?

And why isn't QP= OP-OQ= [ -3, -1, -4 ]?

4. i would most probably used position vector to solve the 1st question:
OQ = (4,3,6)
OP = (1,2,2)

QP = QO + OP
= (-4,-3,-6) + (1,2,2)
= (-3,-1,-4)

5. so we have the same ans for part 1. what about the other two parts?

is it:

|Moment| = | F x QP |
= | -15i+9j+9k |
= sqrt 387

on the right track?

than for last part:

unit vector in the direction of moment==> unit vector parallel with moment==> unit vector of moment.

which is -15i + 9j +9k?

is this the way?