What is the correct angle between two vectors?

[Jamison Lahman]

Homework Statement

From Analytical Mechanics by Grant R. Fowles & George L. Cassiday.

Only problem I am having is with part d.

Homework Equations

##A\cdot B = A_xB_x+A_yB_y+A_zB_z##
##sin(\theta) = \frac{|A\times B|}{AB}##

The Attempt at a Solution

I did it by hand but also ran the following Matlab script:

A = [1,1,1];
B = [1,1,0];
theta = acos(dot(A,B)/norm(A)/norm(B))
theta = asin(norm(cross(A,B))/norm(A)/norm(B))

Both formulas return 0.61548. I think the minus sign in part d should not be there, but I might be missing something. A second pair of eyes would be appreciated.

 

[mfb]

Where do you get the 1-1 in the numerator from?

(1*1)+(1*1)+(1*0)=1+1.

You can also use the result of (c) to get the angle.
(c) doesn't look like a final answer by the way.

 

[Jamison Lahman]

Where do you get the 1-1 in the numerator from?

(1*1)+(1*1)+(1*0)=1+1.

You can also use the result of (c) to get the angle.
(c) doesn't look like a final answer by the way.

The image is the solution from the manual. I used the Matlab code and got and angle of .6 in radians. It appears the solution manual was incorrect.

 

[mfb]

Yes, the solution shown in the second image is wrong.