Question

Use the definition of scalar product, a · b = ab cos θ, and thefact that a · b = axbx + ayby + azbz to calculate the angle betweenthe two vectors given by a = 3.0i + 3.0j + 3.0k and b = 7.0i + 5.0j+ 5.0k.

This is what i have tried thus far:
a = 3.0i + 3.0j + 3.0k
b = 7.0i + 5.0j + 5.0k
a * b = (3*7) + (3*5) + (3*5)
a*b = 51
a*b= |a||b|cosθ
|a| = √(3² + 3² + 3²)
|a| = 5.196
|b| = √(7² + 5² + 5²)

|b| = 9.949

So 51 = 9.949 * 5.196 * cosθ

θ = 45.48 is wrong, also 134.52 does not work. What is wronghere.

Please show all your work. Thanks.