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Answer» Dot Product Properties: - Dot product of two vectors is commutative i.e. a.b = b.a = ab cos θ.
- If a.b = 0 then it can be clearly seen that either b or a is zero or cos θ = 0 ⇒θ = π/2. It suggests that either of the vectors is zero or they are perpendicular to each other.
- Also we know that using scalar product of vectors (pa).(qb)=(pb).(qa)=pq a.b
- The dot product of a vector to itself is the magnitude squared of the vector i.e. a.a = a.a cos 0 = a2
- The dot product follows the distributive law also i.e. a.(b + c) = a.b + a.c
Properties of the Cross Product: - The length of the cross product of two vectors is \(|\vec a\times\vec b|=|a||b|sin\theta\)
- The length of the cross product of two vectors is equal to the area of the parallelogram determined by the two vectors.
- Anticommutativity: \(\vec a\times\vec b=-\vec b\times\vec a\)
- The volume of the parallelepiped determined by the vectors a, b, and c is the magnitude of their scalar triple product
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