Question

1. Suppose that a wind is blowing from the direction N45°W at a speed of 50km/h. A pilo is steering a plane in the direction N60°E at an airspeed (speed in still air) of 250km/h. Find: (5pts) a. The ground speed of the plane (i.e. the magnitude of the resultant of the velocity vectors of the plane and the wind), and The true course of the plane (i.e. the direction of the resultant) b. A box has dimensions 3ft by 5ft by 7ft. Use vectors to find the angle formed by the diagonal of the box and: (5pts) a. The diagonal of the side that measures 3ft by 7f. 2) b. The edge that measures 5ft. points of intersection. (5pts) ; (opts) 4. Given the planes x-z 1 and y + 2z 3 that the nlanes are not parallel. Be specific!

Answer 1

a.

Let side along x axis be 3 ft and side along y axis be 5ft and side along z axis be 7 ft

So the diagonal of box is the vector

D=3i+5j+7k

The diagonal of side measuring 3ft by 7ft is

d=3i+7k

So the angle is given by

D.d=|D||d|cos(x) , x is angle between them

D.d=3^2+7^2=58=|D||d|=sqrt(83)sqrt(58) cos(x)

cos(x)=58/sqrt(83*58)

x~33.29 degrees

b.

edge measuing 5ft has the vector

e=5j

D.e=5^2=|D||e|cos(t) , t is angle between them

25=sqrt(83)sqrt(25)cos(t)

cos(t)=5/sqrt(83)

t~56.71 degrees