a) use a klein model to show the right- and left-sensed parallels to a line l through point p not on l. b) in the same model, show two lines through p that are ultraparallel to l.
A) use a klein model to show the right- and left-sensed parallels to a line l through point p not...
1. Find the point on line L that is closest to point P. (a) L: y = 5x - 4, P = (0,9) (b) L: the line through (-1,6) and (3,0), P = (4,5) You need to (i) Draw a graph (ii) Find the equation of L, if not already given (iii) Find the slope perpendicular to L, slope p=- (iv) Find the equation of the line with this two perpendicular slope through P (v) Interesect the two lines
For the convex hull algorithm we have to be able to test whether a point r lies left or right of the directed line through two points p and q. Let = (px, Py), q , and r-(Tx,rv). a. Show that the sign of the determinant 1 rx iy determines whether r lies left or right of the line.
For the convex hull algorithm we have to be able to test whether a point r lies left or right of...
6. Hyperbolic half-plane model: Consider the line I with equation 2+y2 1 and the point P(2, V3). Describe all the lines through P that are parallel to l. Your answer should be something like (x-a)2 + y2 = r2 with conditions on a and r and/or x = a with conditions on a.
6. Hyperbolic half-plane model: Consider the line I with equation 2+y2 1 and the point P(2, V3). Describe all the lines through P that are parallel to...
72. Points and lines. Let L be the line passing through the points A (1,1,2) and B=(3,5,6). (a) Use a vector projection to find the closest point P on L to the point C = (2,1,1). (b) Find the distance between P and C.
Let L1 be the line passing through the point P 2, 2,-1) with direction vector a=[-1, 1,-2]T, and let L2 be the line passing through the point P2-(-5, -5,-3) with the same direction vector. Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that dQ1Q2) d. Use the square root symbol' where needed to give an exact value for your answer. d 0 Q1-(0, 0, 0)...
(1 point) (A) Find the parametric equations for the line through the point P = (-4, 4, 3) that is perpendicular to the plane 4.0 - 4y - 4x=1. Use "t" as your variable, t = 0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. (B) At what point Q does this line intersect the yz-plane? Q=(
Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r, y.3)r In:+sin(y:)- 0 at p. Then L intersects the plane :-0 at the point
Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r, y.3)r In:+sin(y:)- 0 at p. Then L intersects the plane :-0 at the point
In the MS/P -- L(Y,r) diagram, a shift to the right of L(Y,r) line -- with an unchanged Y -- would cause? Group of answer choices a shift to the right of the IS curve and a shift to the right of the AD curve. a shift to the left of the LM curve but no change to the AD curve. a shift to the right of the LM curve and a shift to the right of the AD curve....
Let L be the line passing through the point P=(4, 5, −2) with direction vector →d=[2, 2, 0]T. Find the shortest distance d from the point P0=(1, 1, −2) to L, and the point Q on L that is closest to P0. Use the square root symbol '√' where needed to give an exact value for your answer.
(1 pt) (A) Find the parametric equations for the line through the point P = (2, 3, 4) that is perpendicular to the plane 2x + 1 y + 3z 1 . Use 't', as your variable, t 0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. X= y- (B) At what point Q does this line intersect the yz-plane?