Answer:
Part 1
The vector can be expressed as follows;
r = 12, θ = 72°, ·v = (12, ∠72°), ·v ≈ 3.71·[tex]\mathbf{\hat i}[/tex] + 11.41·[tex]\mathbf{\hat j}[/tex] or
[tex]\mathbf{\cdot v}=\begin{bmatrix}3.71\\ 11.41\end{bmatrix} = \begin{pmatrix}3.71\\ 11.41 \end{pmatrix}[/tex]
Part 2
The angle of the vector is 56.31°
Explanation:
Part 1
The given parameters are;
The direction of the vector = 72°
The vector magnitude = 12
Therefore, the vector can be described in the following forms;
Polar form
1) Direct notation;
r = 12, θ = 72°
2) Ordered set
·v = (12, ∠72°)
Rectangular vector notation;
1) Unit vector notation
·v = vₓ[tex]\mathbf{\hat i}[/tex] + [tex]v_y[/tex][tex]\mathbf{\hat j}[/tex]
Where;
vₓ = 12 × cos(72) ≈ 3.71
[tex]v_y[/tex] = 12 × sin(72) ≈ 11.41
Therefore;
·v ≈ 3.71·[tex]\mathbf{\hat i}[/tex] + 11.41·[tex]\mathbf{\hat j}[/tex]
2) Matrix notation
[tex]\mathbf{\cdot v}=\begin{bmatrix}3.71\\ 11.41\end{bmatrix} = \begin{pmatrix}3.71\\ 11.41 \end{pmatrix}[/tex]
Part 2
The given vector is V = 2·x + 3·y
Therefore, the angle of the vector, θ = tan⁻¹(y/x) = tan⁻¹(3/2) ≈ 56.31°
The angle of the vector = 56.31°.
