Physics - particle moving in space?
A particle is moving in space. At a particular time, the position vector is r = (i+ 2j + 3k)m, the velocity vector is v = (2j-k) m/s. and the acceleration vector is a = 4k m/s^2.
i, j, k, r, v, and r are vectors
*the speed of the particle
*the vector product (r x v)
*the scalar product (a dot v)
- FredLv 78 years agoFavorite Answer
[You mean, "i, j, k, r, v, and a are vectors"?]
I will use the convention that vectors have an underscore: "v_", except for the coordinate unit vectors, i, j, & k.
Rules for doing vector & scalar products:
ixi=0 . . ixj=k .. ixk=-j
jxi=-k .. jxj=0 .. jxk=i
kxi=j . . kxj=-i . kxk=0
i•i=1 . . i•j=0 . . i•k=0
j•i=0 . . j•j=1 . . j•k=0
k•i=0 .. k•j=0 .. k•k=1
speed = magnitude of the velocity vector
|v_| = √(0^2 + 2^2 + 1^2) m/s = √5 m/s
r_ x v_ = (i + 2j + 3k) x (2j - k) m^2 /s
= (2ixj - ixk - 2jxk + 6kxj) m^2 /s
= (2k + j - 2i - 6i) m^2 /s
= (-8i + j + 2k) m^2 /s
a_•v_ = 4k • (2j - k) m^2 /s^3
= -4 m^2 /s^3