Consider the vector v = 8.69(cos 24.4°î + sin 24.4°j)

1. The cross winds hitting the plane due east is given by the formula as follows. 20 sin 2wt + 30 sin (3wt +) mph The driving wind (to a runway laying due North), directly behind the aircraft is given by the following formula. 10 cos wt - 30 cos (wt+ +7) mph If the course heading of the aircraft is due north, what is its resultant heading? Using vectors, plot the change required in course heading, and help the crew land the plane. You can ignore airspeed, turbulence etc... In addition, using software Model the combination of sine waves graphically and draw the graphical resultants of the waveforms and hence perform a graphical analysis as a comparison between your calculated results and what you have drawn.

Vectors u = −4(cos 60°i + sin60°j), v = 8(cos 135°i + sin135°j), and w = 12(cos 150°i + sin150°j) are given. Use exact values when evaluating sine and cosine. Can u explain in simple terms that way its easier for me to understandPart A: Find −7u ⋅ v. Show your work. Part B: Use the dot product to determine if u and w are parallel, orthogonal, or neither. Justify your answer.