Question

Define scalar product and write any five properties

Answer 1

$\huge\mathfrak\red{Answer}$

Scalar product of two vectors is defined as the product of the magnitude of one vector and the magnitude of the component of other vector in the direction of first vector. Scalar product of two vectors is commutative.

Properties of scalrar product:

• The scalar product of a vector and itself is a positive real number: u → ⋅ u → ⩾ 0 . ...
• The scalar product is commutative: u → ⋅ v → = v → ⋅ u → . ...
• The scalar product is pseudoassociative: α ( u → ⋅ v → ) = ( α u → ) ⋅ v → = u → ⋅ ( α v → ) where is a real number.

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