core 4 question - help?

The points 0(0, 0, 0), A (2, 8, 2), 5(5, 5, 8) and C(3, -3, 6) form a parallelogram OABC.

Use a scalar
product to find the acute angle between the diagonals of this parallelogram

I keep getting 84.5 but the answer gives 81.7 to 82°

I worked it out by finding the vector equations of the lines AB and BC and then using the vector parts of them equations to get exactly root 3 over 18 and then used cos to get the angle

I keep getting 84.5 but the answer gives 81.7 to 82°

What am I doing wrong?

I don't know the mistake in your working unless you post your working in full.

But you don't need to find vector equations of any line. You can find $\vec{AC}$ directly from the vectors you already have. Then dot product $\vec{AC}$ with $\vec{OB}$.

I recommend you draw a diagram if you haven't already - the method should become clear.