Question

If Vx = 7.00 units and Vy = -7.60 units, determine the magnitude of V⃗ .

Answer 1

|V| = 10.33 units and the direction θ = -47.35° or 312.65°.

Given the x and y components of a vector, we can calculate the magnitude and direction from these components.

Applying the Pythagorean theorem we have that the magnitude of the vector is:

|V| = $\sqrt{Vx^{2}+Vy^{2} }$

|V| = $\sqrt{(7.00units)^{2}+(-7.60units)^{2}} = \sqrt{106units^{2}} = 10.33units$

The expression for the direction of a vector comes from the definition of the tangent of an angle:

tan θ = $\frac{Vy}{Vx}$ ------>  θ = arc tan $\frac{Vy}{Vx}$

θ = arc tan $\frac{-7.60units}{7.00units}$

θ = -47.35° or 312.65°