Question
Fri May 18, 2012 By: Avi

Tell all properties of cross and dot vector

Expert Reply
Fri May 18, 2012
Dot Product:: Let a and b be two vectors inRn, then the dot product of a and b is thescalar a · b given by
a · b = a1b1 + a2b2 + a3b3 + · · · + anbn
 
Properties of the Dot Product
If a, b and c are vectors in Rn and c is ascalar then
a · a = |a|2
a·b=b·a
a · (b + c) = a · b + a · c
(c a) · b = c(a · b) = a · (c b)
0 · a = 0.
 
Vectro product:: De?nition:If a = a1, a2, a3 and b =b1, b2, b3, then the cross product of a andb is the vector
a × b = a2b3 ? a3b2, a3b1 ? a1b3, a1b2 ? a2b1
 
Properties of the Cross Product
If a and b and c are vectors and c is a scalar,then1) a × b = ?b × a
2) (ca) × b = c(a × b) = a × (cb)
3) a × (b + c) = a × b + a × c
4) (a + b) × c = a × c + b × c
5) a · (b × c) = (a × b) · c
6) a × (b × c) = (a · c)b ? (a · b)c
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