Answer All Questions for All Points (1500!) (A) Consider the planes 4x + 5y + 2z
ID: 2871291 • Letter: A
Question
Answer All Questions for All Points (1500!)
(A)
Consider the planes 4x + 5y + 2z = 1 and 4x + 2z = 0.
(1) Find the unique point P on the y-axis which is on both planes. (___?,___? ,___?)
(2) Find a unit vector u with positive first coordinate that is parallel to both planes.
____i + ____ j + ____ k
Use parts those two answers (1 and 2) to find a vector equation for the line of intersection of the two planes,
r(t)= _____i + ____ j + ____ k
(B)
Find an equation of the plane consisting of all points that are equidistant from (3, 0, 3) and (5, 4, -1).
________________________ ?
(C)
A million years ago, an alien species built a vertical tower on a horizontal plane. When they returned they discovered that the ground had tilted so that measurements of 3 points on the ground gave coordinates of (0, 0, 0), (2, 2, 0), and (0, 2, 2). By what angle does the tower now deviate from the vertical?
(D)
Find the angle of intersection of the plane -1x - 1y + 1z = 5 with the plane -3x - 1y - 5z = 2 .
Answer in radians = _________ ?
Answer in degrees = _________ ?
(E)
Determine whether the lines
L 1 : x= 22 + 7t, y= 2 + t , z= 25 + 7t
and
L 2 : x= -15 + 8t, y= -7 + 3t, z= -16 + 10t
Apparently these lines DO INTERSECT. Please find the point of intersection.
Point of intersection: (___, ___, ___)?
Explanation / Answer
doing