Mention any three properties of scalar product of two vectors.
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Properties of the scalar 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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In geometry, Keller's conjecture is the conjecture that in any tiling of Euclidean space by identical hypercubes there are two cubes that meet face to face. For instance, as shown in the illustration, in any tiling of the plane by identical squares, some two squares must meet edge to ed
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