Finding The Angle With Dot Product and Cross Product

[Ted_Grendy]

Hi all

I am trying to obtain the angle between two vectors from the dot product and cross product.

My vectors are:-

A = [4, -5, 6]
B = [-1, 5, 1]

From the dot product I get:-

A dot B = -23
Modulus A = Sqrt(77)
Modulus B = 3Sqrt(3)
Theta = arcos(-23/ Sqrt(77) * 3Sqrt(3))
Theta = 120.293


However with the Cross product I get:-

AXB = [-35, -10, 15]
Modulus AXB = 5Sqrt(62)
Modulus A = Sqrt(77)
Modulus B = 3Sqrt(3)
Theta = arsine(5Sqrt(62) / Sqrt(77) * 3Sqrt(3)]
Theta = 59.7065

I get two different answers - what I am doing wrong? can anyone help?


Thank you.

 

[tkhunny]

Did you notice that 120.293 + 59.7065 = 179.9995?

Are you SURE you know what is meant by: x / y * z ?? Is it [math]\dfrac{x}{y\cdot z}\;or\;\dfrac{x}{y}\cdot z[/math]? You're going to have to make up your mind.

 

[Dr.Peterson]

Do you notice how your two answers, 120.293 and 59.7065 are related? (Hint: try adding them.)

Are you aware that the arcsin is only one of two angles with a given sine? (This may remind you of the "ambiguous case" in solving triangles.)