The vector V is at a 72° angle and has a magnitude of 12. Describe this vector using vector notation (Use the & and symbols.) (6 points)
Question 9
What is the angle of the vector described below? (3 points).
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V=2x+3y

Part 1

The vector can be expressed as follows;

r = 12, θ = 72°, ·v = (12, ∠72°), ·v ≈ 3.71· + 11.41· or

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 +

Where;

vₓ = 12 × cos(72) ≈ 3.71

= 12 × sin(72) ≈ 11.41

Therefore;

·v ≈ 3.71· + 11.41·

2) Matrix notation

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°.

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