Q.Write the properties of Vector Product. (Any six)

The vector product A x B is a vector, is anti-commutative, is distributive, vanishes for parallel vectors or a vector crossed with itself, and follows the right-hand-rule cyclic pattern for unit vectors.

1. Vector nature: Unlike the dot product (which gives a scalar), the cross product A x B is itself a VECTOR quantity, with magnitude |A x B| = |A||B| sin(theta), where theta is the angle between A and B.

2. Direction (right-hand rule): The direction of A x B is perpendicular to the plane containing both A and B, determined by curling the right-hand fingers from A to B -- the thumb points along A x B.

3. Not commutative (anti-commutative): A x B = -(B x A). Reversing the order of the vectors reverses the direction of the resulting vector.

4. Distributive over addition: A x (B + C) = (A x B) + (A x C).

5. Self cross product is zero: A x A = 0, since the angle between a vector and itself is 0 degrees, and sin(0) = 0.

6. Cross product of parallel/antiparallel vectors is zero: if A and B are parallel (theta=0) or antiparallel (theta=180), sin(theta)=0, so A x B = 0.

7. Not associative in general: A x (B x C) is not equal to (A x B) x C.

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