Page 4 - Lesson Notes (Motion in a Plane)
P. 4
(vii) Scalar product in cartesian coordinates
= A xB x + A yB y + A zB z
Vector or Cross Product of Two Vectors
The vector product of two vectors is equal to the product of their magnitudes and the
sine of the smaller angle between them. It is denoted by * (cross).
A * B = AB sin θ n
The direction of unit vector n can be obtained from right hand thumb rule.
If fingers of right hand are curled from A to B through smaller angle between them, then
thumb will represent the direction of vector (A * B).
The vector or cross product of two vectors is also a vector.
Properties of Vector Product
(i) Vector product is not commutative, i.e.,
A * B ≠ B * A [∴ (A * B) = — (B * A)]
(ii) Vector product is distributive, i.e.,
A * (B + C) = A * B + A * C
(iii) Vector product of two parallel vectors is zero, i.e.,
A * B = AB sin O° = 0
(iv) Vector product of any vector with itself is zero.
A * A = AA sin O° = 0
(v) Vector product of orthogonal unit vectors
