Question

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

Determine the direction 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 =
`(Vy)/(Vx)` ------> θ = arc tan
`(Vy)/(Vx)`

θ = arc tan
`(-7.60units)/(7.00units)`

θ = -47.35° or 312.65°