Find Position Vector?

Question

The vector v has the initial point P and the terminal Point Q.
Write v in the form ai + bj + ck; that is, find its position vector.

(1) P = (0, 0, 0); Q = (-3, -5, 4)

(2) P = (-1, 4, -2); Q = (6, 2, 2)

Answer 1

position vectors are:
if you have two points
p(0,0,0) and q (-3,-5,4)
then it is
the vector PQ which is found by subrating each each value (x,y,z) of P from the values of Q
what i mean is
you subtract the x,y,and z coordinates of point P from Point q:
so
-3-0= 0, -5-0 = -5 and soo on..
whhich then becomes:
pq(-3,-5,4) this in i,j,k form:
i is the x value
j is the y
and k is the z value so
-3i-5j+4k
the same applies for the second one:
which is Q-P
which is then
(6- -1) which is 7, 2-4, which is -2 and 2--2 which is 4 hence :
(7,-2,4)
7i-2j+4k

Answer 2

I rejoice with your question and learn from Calzrhe's answer. I placed my answer in a different way. seem whilst an gadgets is shifting in a airplane and that i ask you to uniquely detrmine that airplane wherein it incredibly is shifting via a vector what's going to you %. As Calzrhe says, a perpendicular course to the airplane seems teh handy way, yet there are 2 perpendiculars, so we've convention to define ?Xr as v, the place ?, r and v are all vectors. Now coming on your 2nd question sure there is a few thing, quite yet another stressful vector in that course referred to as angular momentum, Vector L defined as rXp, the place p is the linear momentum vector. via finding out like this we've have been given some sort of analogous similarity between linear and angular action. in case you stretch the analogy too lots then there are a number of stressful issues you will face. yet pl don't get aggravated use it and attempt to take exhilaration in teh annoyance. As Feynman says approximately QM take it with no attention that it works please do no longer ask why because of fact no person is familiar with it! Intricacies of physics initiate actual in classical Physics it self. you assert no longer something is going on in perpendicular course. ok, take rotating wheel on an axle carry the axle on your 2 palms. Wheel is rotating no longer something is going on alongside the axle. Now attempt rotate the axle and sense which you detect project in balancing your self. So inspite of each little thing some thing is ingredient is there in perpendicular course and that someting additionally facilitates the wheel to rotate because it rotates.

Answer 3

The position vector will be represented by Q-P for each component.
For these problems,
1) v=-3i-5j+4k

2) v=7i-2j+4k

Answer 4

Use r for position vector
(v is usually used for velocity)

Question 1
r = - 3i - 5j + 4

Question 2
r = 7i - 2j + 4k