What angle is between **a** = (4,4,4)^{T} and **b** = (4,0,4)^{T}?

Visually, it looks somewhat less than midway between perpendicular and horizontal. 35° would be a good guess.

To do better than guessing, notice that in going from the
tail to the head of **a** the vertical distance increases by 4
while the horizontal distance increases by 4 √2.

Hence the tangent of the angle is 4 / (4 √2) = 1.0/ √2 = 0.7071.

so the angle with the horizontal is arctan( 0.7071 ) = 35.26°.
Since **b** is in the horizontal plane,
the angle between the two vectors must be that value.

The formula for the angle θ between two unit vectors is:

a= cosθ_{u}· b_{u}

To use this formula with non-unit vectors:

- normalize each vector,
- compute the dot product,
- use the arc cos to get the angle.

(Calculator Problem: )
Apply this formula to **a** and **b** of the figure.

- Vector
**a**is represented by (4,4,4)^{T} - Vector
**b**is represented by (4,0,4)^{T}