Question

Find the magnitude and direction of this vector

Answer 1

(174^2 + 88.4^2)^1/2 = 195 m magnitude of resultant vector

(tan θ = 88.4 / 174 = .508 or 26.9 deg)

Answer 2

The magnitude of the vector is approximately 195.17m and its direction is approximately 26.933°.

To calculate the magnitude of this vector using pythagora s theorem,

|V| =
`\sqrt{longitude^(2) +latitude^(2) }`

Where longitude = 174m

Latitude = 88.4m

|V| =
`\sqrt{174^(2) +88.4^(2) }`

|V| =
`√(30276+7814.56)`

|V| =
`√(38090.56)`

|V| = 195.17 m to 2 dp

To calculate the direction of the vector,

Direction =
`tan^(-1)`
`(Latitude)/(Longitude)`

Direction =
`tan^(-1)` 88.4/174

Direction =
`tan^(-1)` 0.50504597701

Direction = 26.933° to 3 dp

Therefore, the magnitude of the vector is approximately 195.17m and its direction is approximately 26.933°.