Question

A vector has an x component of -27.5 units and a y component of 41.4 units. Find the magnitude and direction of this vector. magnitude _________ unit(s) direction _____________ º counterclockwise from the +x axis

Answer 1

a.) magnitude __49.7__ unit(s)

b.) direction __123.6°_ counterclockwise from the +x axis

Step-by-step explanation:

Let Vector is v

x-component of Vector v = x = -27.5 units (minus sign indicate that x-component is along the minus x-axis )

y-component of Vector v = y = 41.4 units

Magnitude of v = ?

Direction of v = ?

To find the magnitude of the vector

v =
`\sqrt{x^(2)+y^(2)  }`

v =
`\sqrt{-27.5^(2)+41.4^(2) }`

v = 49.7 units

To find direction

θ = tan⁻¹(y/x)

θ = tan⁻¹(41.4/-27.5)

θ = -56.4°

This Angle is in the clockwise direction with respect to -x axis.

We need to find Angle counterclockwise from the +x axis.

So,

θ = 180° - 56.4°

θ = 123.6°

The given vector is in 2nd quadrant