Dot product and angles practice problems

Let \( \displaystyle \mathbf{u} = \langle 1, 3, 0 \rangle \) and \( \displaystyle \mathbf{v} = \langle 3, -4, -5 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -1, 3, -3 \rangle \) and \( \displaystyle \mathbf{v} = \langle 0, 4, 0 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 0, -4, -4 \rangle \) and \( \displaystyle \mathbf{v} = \langle 5, 3, -4 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 4, -5, -2 \rangle \) and \( \displaystyle \mathbf{v} = \langle -4, 1, -2 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -3, 4, 0 \rangle \) and \( \displaystyle \mathbf{v} = \langle -1, -2, 2 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -1, 3, 4 \rangle \) and \( \displaystyle \mathbf{v} = \langle 0, 2, -5 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 4, 2, 1 \rangle \) and \( \displaystyle \mathbf{v} = \langle 0, 2, 5 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -2, 0, -2 \rangle \) and \( \displaystyle \mathbf{v} = \langle 2, 4, -2 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 2, 1, 5 \rangle \) and \( \displaystyle \mathbf{v} = \langle -1, 3, 5 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 0, -1, -5 \rangle \) and \( \displaystyle \mathbf{v} = \langle 2, -2, 1 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -2, 1, -2 \rangle \) and \( \displaystyle \mathbf{v} = \langle 1, 5, 4 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -1, -3, 0 \rangle \) and \( \displaystyle \mathbf{v} = \langle 5, -1, 5 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 4, -4, 4 \rangle \) and \( \displaystyle \mathbf{v} = \langle 2, -5, -5 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -1, 4, 2 \rangle \) and \( \displaystyle \mathbf{v} = \langle 3, -4, 2 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -1, -5, 1 \rangle \) and \( \displaystyle \mathbf{v} = \langle 2, -2, 4 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 0, 5, -1 \rangle \) and \( \displaystyle \mathbf{v} = \langle -1, 3, -5 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 4, 0, -3 \rangle \) and \( \displaystyle \mathbf{v} = \langle 1, 0, -1 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 5, -1, 2 \rangle \) and \( \displaystyle \mathbf{v} = \langle 4, 2, -4 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -1, 2, 5 \rangle \) and \( \displaystyle \mathbf{v} = \langle 0, -5, 4 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 1, 4, 1 \rangle \) and \( \displaystyle \mathbf{v} = \langle 2, 0, -1 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 4, 1, -5 \rangle \) and \( \displaystyle \mathbf{v} = \langle 5, -4, -3 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -4, 0, -2 \rangle \) and \( \displaystyle \mathbf{v} = \langle -3, -5, -5 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -3, 5, 5 \rangle \) and \( \displaystyle \mathbf{v} = \langle 5, 1, -3 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -4, 5, -4 \rangle \) and \( \displaystyle \mathbf{v} = \langle -4, 1, -3 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 0, 5, -5 \rangle \) and \( \displaystyle \mathbf{v} = \langle 3, -1, -3 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 0, -4, -4 \rangle \) and \( \displaystyle \mathbf{v} = \langle 5, -1, -4 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -4, 3, 4 \rangle \) and \( \displaystyle \mathbf{v} = \langle 0, -2, 5 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -4, 2, -3 \rangle \) and \( \displaystyle \mathbf{v} = \langle 5, 4, -2 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle -1, 0, 3 \rangle \) and \( \displaystyle \mathbf{v} = \langle -3, -5, 3 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.

Let \( \displaystyle \mathbf{u} = \langle 0, 1, -5 \rangle \) and \( \displaystyle \mathbf{v} = \langle -1, 1, 3 \rangle \). Find \( \displaystyle \mathbf{u} \cdot \mathbf{v} \) and the angle between them.