Q: Why you only use cosine for scalar product?

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Normally you use sine theta with the cross product and cos theta with the vector product, so that the cross product of parallel vectors is zero while the dot product of vectors at right angles is zero.

Dot Products in Physics denote scalar results fmo vector products, e.g Work = F.D = FDCos(FD) a scalar result from the dot product of two vectors, F Force and D Displacement.

Use the appropriate sine or cosine ratio.

cosine = adjacent/hypotenuse. It can be used as other trig functions can.

use the inverse sine or cosine or tangent

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Some Physics definitions ignore the real world of Nature. Forces and distances are four dimensional including real and vector quantities. Work is defined as the scalar product of two vectors and ignores the scalar cross distances and vector cross products..Gravity is a scalar force and gravitatinal potential energy is mgh where mg is a scalar force and h is a scalar distance. This is not called work because it is not the scalar product of two vectors.Nature and Physics involves scalar and vector quantities, in other words Quaternion quantities. The Quaternion product of force and distance is:(f + F)(d + D) = (fd - F.D) + (fD + dF + FxD).Physics only defines work as F.D and ignores the other 'work' including Torque,FxD.

Normally you use sine theta with the cross product and cos theta with the vector product, so that the cross product of parallel vectors is zero while the dot product of vectors at right angles is zero.

In physics, a scalar is a quantity that has only magnitude, without a direction. For example, temperature is a scalar quantity because it only has a value (e.g., 25 degrees) without needing a direction.

pen0r

Dot Products in Physics denote scalar results fmo vector products, e.g Work = F.D = FDCos(FD) a scalar result from the dot product of two vectors, F Force and D Displacement.

Use the appropriate sine or cosine ratio.

cosine = adjacent/hypotenuse. It can be used as other trig functions can.

use the inverse sine or cosine or tangent

To multiply two vectors in 3D, you can use the dot product or the cross product. The dot product results in a scalar quantity, while the cross product produces a new vector that is perpendicular to the original two vectors.

If you do not know only a side length you cannot. If you know all three side lengths then you can use the cosine rule. You can continue using the cosine rule for the other two angles but, once you have one angle, it is simpler to use the sine rule.

It depends on what information you have. If you have only the lengths of the three sides, you would need to use the cosine rule.

Trigonometry