1) For points P(1, -2, 1) , Q(0, -2, 5) and R(4, -6, 7) ,
a) Find the vector v from point P to point Q?
b) Find the vector k from R to P?
c) Calculate the dot product of v and k.
d) Calculate the cross product of v and k.
e) The projection of v on k.
f) The angle between v and k.
For question 1, Write a MATLAB program to verify your answers. Submit the output displayed.(Use matlab functions such as dot, cross, norm, acos)
2) Solar panels have to be installed carefully so that the tilt of the roof and direction to the sun rays should maximize the power absorbed from the sun.
Here are the coordinates of the corners of the roof at the picture P1(8,6,4) , P2(8,10,4), P3(6,8,8) and P4(6,4,8). Determine the following for this roof.
a) What are the edge vectors that define the roof surface? Write them in component form.
b) What is the unit vector (p) perpendicular to these edge vectors of the roof surface?
c) If the flow of solar energy is in s=[4 -3 2] direction with magnitude of 1000 watts/meter2, calculate the dot product of E=1000us and p. (where us is the unit vector of s).
d) Calculate the angle between s and p. What do you say about this angle for maximum solar energy?
3) Find the unit vector perpendicular to the plane -3x + 7y - 2z = 8.
4) A wheel is rotating about x-axis with angular speed w=20sec-1 (you can take this quantity as it is, no need to transform to rads/sec, the units for this angular speed is revolutions/secs) The rotation is clockwise if one sits at the origin and looks at this wheel in the positive x direction. Find the velocity and speed at point [4 3 0]. Make a sketch.
5) Two forces of equal magnitude are applied to the wrench. If a moment of 50N-m is required to loosen the nut and determine the Force vectors.
