Question

Let v = leftanglebracket 3, negative 2 rightanglebracket. what is the approximate direction angle of v?

Answer 1

The approximate direction angle of v is 326°

Definition of Direction Angle

A vector's direction angle is the angle formed by the positive x-axis and the vector v. The arctangent of the ratio between the vertical and horizontal components of the vector, v=xi+yj, can be used to determine the direction angle, θ.

What is the direction angle of v?

Let θ be the direction angle of v or the angle mad by v with the horizontal line.

It is given that,

$v = < 3, -2 >$

We know that,

θ = tan⁻¹($\frac{y}{x}$)

Here, we have y = -2 and x = 3. Hence, we get,

∴ θ = tan⁻¹$(\frac{-2}{3})$

⇒θ = tan⁻¹(0.66)

Hence the direction angle of v = 360 - tan⁻¹(0.66)

≈ 326°

Thus, the approximate direction angle of v is 326°.

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