Question

Why we use cos in dot product and sin in cross product..​

Answer 1

The distance is covered along one axis or in the direction of force and there is no need of perpendicular axis or sin theta. In cross product the angle between must be greater than 0 and less than 180 degree it is max at 90 degree. ... That's why we use cos theta for dot product and sin theta for cross product.

thanks...

Answer 2

Concept

Dot product defines the sum of products of corresponding terms of a sequence or equations

Given

Sin in cross product and Cross in dot product.

Find

why do we use such conventions.

Solution

In dot product we use cos theta because in this type of product

1.) One vector is the projection over the other.

2.) The distance is covered along one axis or in the direction of force and there is no need of perpendicular axis or sin theta. In cross product the angle between must be greater than 0 and less than 180 degree it is max at 90 degree. let take the example of torque if the angle between applied force and moment arm is 90 degree than torque will be max. That's why we use cos theta for dot product and sin theta for cross product.

Whenever perpendicular is involved we must take crossproduct.

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