Question

Define vector product eplxain the properties of a vector product

Answer 1

vector product: vector c whose length is the product of the lengths of two vectors a and b and the sine of their included angle, whose direction is perpendicular to their plane, and whose direction is that in which a right-handed screw rotated from a toward b along axis c would move called also cross product

i) The vector product never has a Commutative Property. It is denoted by,

a×b = – (b×a)

ii) The property given below is true in the case of vector multiplication:

(ka)×b= k(a×b) =a×(kb)

iii) If the vectors mentioned are collinear then

a×b= 0

(Since the angle between both the vectors would be 0, then sin 0 = 0)

iv) a × b in terms of unit vectors can be represented as

a =a1^i+a2^j+a3^k

b =b1^i+b2^j+b3^k

Then →a×→b =(a1^i+a2^j+a3^k)(b1^i+b2^j+b3^k)

When expanded, we would get

|a||b|sinθ ^n = (a2b3–a3b2)^i+(a3b1–a1b3)^j+(a1b2–a2b1)^k

v) Distributive Law: a×(b+c) = a×b+a×c