Resultant direction of aircraft

[gkraju]

Homework Statement

in a control configured aircraft the wind is oriented along V= 2i+7j+20k and with a magnitude of 45 knots. the aircraft is controlled to point along vector X = 4i+7j+3k at a speed of 2450 knots. Find the direction and magnitude of aircraft velocity vector ?

Homework Equations

The Attempt at a Solution

i calculated unit vector of direction of wind.
also i calculated unit vector of direction of aircraft
i do not know what to do afterwards ?

 

[berkeman]

Homework Statement

in a control configured aircraft the wind is oriented along V= 2i+7j+20k and with a magnitude of 45 knots. the aircraft is controlled to point along vector X = 4i+7j+3k at a speed of 2450 knots. Find the direction and magnitude of aircraft velocity vector ?

Homework Equations

The Attempt at a Solution

i calculated unit vector of direction of wind.
also i calculated unit vector of direction of aircraft
i do not know what to do afterwards ?

What is the velocity vector of the plane? What happens if you add the velocity vectors of the wind and plane?

 

[HallsofIvy]

A "velocity vector" should point in the right direction and its length should be the speed. After you have found the unit vectors in each direction, multiply by the given speed (45 knots for the winds speed, 2450 knots for the airplane [Which is, by the way, about 4 times the speed of sound- what kind of airplane is this?]) to get the actual velocity vectors. Then, as berkeman says, add them by adding the corresponding components.