Angle Between 2 Vectors Definition of Scalar Product Important Properties Scalar Product In Cartesian Form Applications of Scalar Product Link To Other Sites

ngle Between 2 Vectors

Let a and b be two non-zero vectors represented by OA and OB respectively. The angle between a and b is defined to be the angle between OA and OB, i.e. � AOB.

efinition of Scalar Product

The scalar product of two non-zero vectors a and b, denoted by a.b, is defined as

mportant Properties

1. a.b = 0 � a ^ b (if a � 0, b � 0)
2. |a.b| = |a||b| � a // b (if a � 0, b � 0)
3. a.b = b.a
4. a.(b + c) = a.b + a.c
5. (la).b = l(a.b) = a.(lb) where l � R.
6. a.a = |a|²

For the 3 mutually perpendicular unit vectors i, j, k, we have
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calar Product in Cartesian Form

Let a = a₁i + a₂j + a₃k, b = b₁i + b₂j + b₃k.� Then, using the properties of scalar product, we have

pplications of Scalar Product

1.��� To prove any two non-zero vectors are perpendicular
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2.��� To find the angle between two non-zero vectors.
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3.��� To find the projection of one vector on another.
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To Other Sites

• Dot (Inner or Scalar) Product

• Scalar Product of Vectors

• Scalar Product

• The scalar or dot product

• Scalar Product

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