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# 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

Calculate:

*the speed of the particle

*the vector product (r x v)

*the scalar product (a dot v)

### 1 Answer

- 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

vector product,

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

scalar product,

a_•v_ = 4k • (2j - k) m^2 /s^3

= -4 m^2 /s^3

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