Question #15212

why we take sin in cross product & cos in dot product?

Expert's answer

Definition of cross product says that it is another vector, that is

perpendicular to each of given vectors and this 3 vectors have right

orientation, and length of third vector is equal product of lengths of

first two vectors and sine of angle between them.

Other words length of vector

cross-product is area of parallelogram built on given 2 vectors.

Since area

of parallelogram includes sine in its formula, then we take sine.

In dot

product we take projection& of the first vector on another one, and that is

why we used cosine.

perpendicular to each of given vectors and this 3 vectors have right

orientation, and length of third vector is equal product of lengths of

first two vectors and sine of angle between them.

Other words length of vector

cross-product is area of parallelogram built on given 2 vectors.

Since area

of parallelogram includes sine in its formula, then we take sine.

In dot

product we take projection& of the first vector on another one, and that is

why we used cosine.

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