Use the definition of scalar product, a · b = ab cos , and the fact that a · b =

Question

Use the definition of scalar product, a · b = ab cos , and the fact that a · b = axbx + ayby + azbz to calculate the angle between the 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|cos
|a| = (32 + 32 + 32)
|a| = 5.196
|b| = (72 + 52 + 52)

|b| = 9.949

So 51 = 9.949 * 5.196 * cos

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

Please show all your work. Thanks.

Explanation / Answer

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|cos? |a| = v(32 + 32 + 32) |a| = 5.196 |b| = v(72 + 52 + 52) |b| = 9.949 So 51 = 9.949 * 5.196 * cos? Here YOU WENT WRONG COS INVERSE OF (51 / 9.949 * 5.196)=9.7351 DEGREE ? = 45.48 is wrong, also 134.52 does not work. What is wrong here.

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