mfb said:What do you know about the magnitude of scalar and vector product as function of the vectors and their angle?
That is true for every angle. ##\sin##, ##\cos## and ##\tan## are just functions of an angle. It doesn't matter where the angle is.andylatham82 said:If we were talking about a right-angled triangle, we could say sin/cos = tan, but that's not the case here is it?
Good so far.andylatham82 said:I can combine the two equations to give
(sin θ)/(cos θ) = (|AxB|)/AB)
You consider functions - there is no triangle involved. The tangent function is defined as this ratio.But I'm not sure where to go next. If we were talking about a right-angled triangle, we could say sin/cos = tan, but that's not the case here is it?
That does not work. ##\sin^{-1} \left( \frac{\sin x}{\sin y} \right) \neq \frac{x}{y}##.I could do cos θ = sin (90-θ) perhaps but my algebra is failing me in reducing the result to an expression giving θ.
θ/(90-θ) = sin-1(|AxB|/AB)
SlowThinker said:That is true for every angle. ##\sin##, ##\cos## and ##\tan## are just functions of an angle. It doesn't matter where the angle is.
To find the angle between two vectors using the dot product, first calculate the dot product of the two vectors. Then, use the formula cosθ = (a · b) / (|a| * |b|) to find the cosine of the angle θ. Finally, use inverse cosine (arccos) to find the angle in radians or degrees.
The dot product of two vectors results in a scalar value, while the cross product of two vectors results in a vector. The dot product measures the similarity or projection of one vector onto another, while the cross product measures the perpendicularity between two vectors.
No, the cross product does not directly give the angle between two vectors. However, you can use the cross product and the magnitude of the two vectors to find the sine of the angle between them, and then use inverse sine (arcsin) to find the angle in radians or degrees.
Yes, there are a few special cases to keep in mind. If the dot product is zero, the two vectors are perpendicular and the angle between them is 90 degrees. If the cross product is zero, the two vectors are parallel and the angle between them is either 0 or 180 degrees. Additionally, the order of the vectors in the cross product matters, as switching the order will result in a vector with the same magnitude but opposite direction.
Yes, you can use the dot and cross product to find the angle between multiple vectors by finding the dot or cross product of every pair of vectors, and then using the appropriate formula to calculate the angle between each pair. Keep in mind that the angle between multiple vectors will be dependent on the order in which they are multiplied, so it may be helpful to use a diagram or visualize the vectors in 3D space.