What do you understand by scalar and vector product of two vectors? Write the formula, explaining the symbols used
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The cross product accumulates interactions between different dimensions. Taking two vectors, we can write every combination of components in a grid:

This completed grid is the outer product, which can be separated into the:
Dot product, the interactions between similar dimensions (x*x y*y, z*z)
Cross product, the interactions between different dimensions (x*y,y*z, z*x, etc.)
The dot product (vec(a) · vec(b)) measures similarity because it only accumulates interactions in matching dimensions. It’s a simple calculation with 3 components.
The cross product (written vec(a) times vec(b)) has to measure a half-dozen “cross interactions”. The calculation looks complex but the concept is simple: accumulate 6 individual differences for the total.
Instead of thinking “When do I need the cross product?” think “When do I need interactions between different dimensions?”.
Area, for example, is formed by vectors pointing in different directions (the more orthogonal, the better). Indeed, the cross product measures the area spanned by two 3d vectors

This completed grid is the outer product, which can be separated into the:
Dot product, the interactions between similar dimensions (x*x y*y, z*z)
Cross product, the interactions between different dimensions (x*y,y*z, z*x, etc.)
The dot product (vec(a) · vec(b)) measures similarity because it only accumulates interactions in matching dimensions. It’s a simple calculation with 3 components.
The cross product (written vec(a) times vec(b)) has to measure a half-dozen “cross interactions”. The calculation looks complex but the concept is simple: accumulate 6 individual differences for the total.
Instead of thinking “When do I need the cross product?” think “When do I need interactions between different dimensions?”.
Area, for example, is formed by vectors pointing in different directions (the more orthogonal, the better). Indeed, the cross product measures the area spanned by two 3d vectors
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scalar means the path which only have magnitude
vector means the path which has magnitude as well as direction
vector means the path which has magnitude as well as direction
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