The vector that represents the resultant velocity of the plane will be V = 30.72 i + 135.89 j + 53.46 k.
<h3>What is a vector?</h3>
The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.
An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of 18° relative to the horizontal. The wind is blowing with a velocity of 42 miles per hour at an angle of S 47° E.
Let north be the y-axis and east be the x-axis. Then the vector equation will be given as,
V = (42 sin 47°) i + (173 cos 18° - 42 cos 47°) j + (173 sin 18°) k
V = 30.72 i + 135.89 j + 53.46 k
The complete question is attached below.
More about the vector link is given below.
brainly.com/question/13188123
#SPJ4