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6. Hyperbolic half-plane model: Consider the line I with equation 2+y2 1 and the point P(2, V3). ...
Recall that the upper half plane H ((x, y)ly > 0) gives a "model" for hyperbolic space. In this m...
Recall that the upper half plane H ((x, y)ly > 0) gives a "model" for hyperbolic space. In this model, distance decreases as one moves up (i.e. the distance between (0, 1) and (1, 1) is 1, the distance between (0,2) and (1,2) is 1/2, and the distance between (0, y) and (1, y) is 1/y. Draw a picture to see that this is strange.) The geodesics on H are given by (1) half circles with center somewhere on the...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i =...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
6. Consider the sphere S cut out by z2 + y2 22. Maximize (Daf)P where y, z) 2y +3z and u is a unit vector in the tangent plane to S at the point (A) v3 (E) 2v3 (B) 1+2V2 (C) 2 v3 (G) 3/2 (D) V2...
6. Consider the sphere S cut out by z2 + y2 22. Maximize (Daf)P where y, z) 2y +3z and u is a unit vector in the tangent plane to S at the point (A) v3 (E) 2v3 (B) 1+2V2 (C) 2 v3 (G) 3/2 (D) V2
6. Consider the sphere S cut out by z2 + y2 22. Maximize (Daf)P where y, z) 2y +3z and u is a unit vector in the tangent plane to S at the...
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this...
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this plane with the plane x = 0. [10 marks] (b) Find the directional derivative of the function F(x, y, z) = 2x /zy2 , at the point P : (1, −1, −2) in the direction of...
Question 9: Plane through point and line A plane contains the point P(-1,2,3) and the line...
Question 9: Plane through point and line A plane contains the point P(-1,2,3) and the line L(t), where L(t) is given by equation (2, 4t - 3,1 – 4t). Find the equation of this plane. Type in the equation of the plane with the accuracy of at least 3 significant figures for each coefficient 1 ) x + ( Dy+ ( )= / Save & Grade Save only
(1 pt) Find a vector equation for the line through the point P = (1, -2,...
(1 pt) Find a vector equation for the line through the point P = (1, -2, 3) and parallel to the vector v = (-3, 2, -3). Assume r(0) = li – 2 + 3k and that v is the velocity vector of the line.. r(t) = i + j+ Rewrite this in terms of the parametric equations for the line. X < N
I cannot get i) or j) 3. (20 marks) Consider the parallel lines L, : x=...
I cannot get i) or j)
3. (20 marks) Consider the parallel lines L, : x= -3 +8 2 [1] and L2: x = 0 + [2] 4. and 11 [3 -21 the planes P1 : 3x + 2y + 2z = -7 and P2 : 2.x – 2y - 2 = 11. (a) Find the equation of a plane in standard form containing both L, and L. (b) Find an equation of the line of intersection of P, and...
The Moulton Plane is the plane M = (R2, LM) such that a subset I of...
The Moulton Plane is the plane M = (R2, LM) such that a subset I of R2 belongs to LM if and only if one of the following holds: i) l = {(x,y)| x=a} (vertical line); ii) l = {(x,y)| y=b} (horizontal line) iii) ( = {(x,y)| y = mx +b where m<0} (line with negative slope) [ m(x - x0) if x xo when m>0}. (bent line W 14,9 m ( x - x0) if x > xo with...
Find the scalar equation for the plane passing through the point P(-1,0,5) and containing the line...
Find the scalar equation for the plane passing through the point P(-1,0,5) and containing the line L defined by x = 4-6t y=-2+2t z=4-2t
equation of the plane
Find the equation of the plane through the point (2,5,7) that is parallel to the line r = (3i + 2j - 2k) + t(i + 2j + 6 k) and perpendicular to the plane 4x + 5y + 6z= 14. Write the equation in the form indicated.Equation: ? (x - 2) + ? (y - ? ) -3(z - ? ) = 0
Recall that the upper half plane H ((x, y)ly > 0) gives a "model" for hyperbolic space. In this model, distance decreases as one moves up (i.e. the distance between (0, 1) and (1, 1) is 1, the distance between (0,2) and (1,2) is 1/2, and the distance between (0, y) and (1, y) is 1/y. Draw a picture to see that this is strange.) The geodesics on H are given by (1) half circles with center somewhere on the...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
6. Consider the sphere S cut out by z2 + y2 22. Maximize (Daf)P where y, z) 2y +3z and u is a unit vector in the tangent plane to S at the point (A) v3 (E) 2v3 (B) 1+2V2 (C) 2 v3 (G) 3/2 (D) V2
6. Consider the sphere S cut out by z2 + y2 22. Maximize (Daf)P where y, z) 2y +3z and u is a unit vector in the tangent plane to S at the...
Question 9: Plane through point and line A plane contains the point P(-1,2,3) and the line L(t), where L(t) is given by equation (2, 4t - 3,1 – 4t). Find the equation of this plane. Type in the equation of the plane with the accuracy of at least 3 significant figures for each coefficient 1 ) x + ( Dy+ ( )= / Save & Grade Save only
(1 pt) Find a vector equation for the line through the point P = (1, -2, 3) and parallel to the vector v = (-3, 2, -3). Assume r(0) = li – 2 + 3k and that v is the velocity vector of the line.. r(t) = i + j+ Rewrite this in terms of the parametric equations for the line. X < N
I cannot get i) or j)
3. (20 marks) Consider the parallel lines L, : x= -3 +8 2 [1] and L2: x = 0 + [2] 4. and 11 [3 -21 the planes P1 : 3x + 2y + 2z = -7 and P2 : 2.x – 2y - 2 = 11. (a) Find the equation of a plane in standard form containing both L, and L. (b) Find an equation of the line of intersection of P, and...
The Moulton Plane is the plane M = (R2, LM) such that a subset I of R2 belongs to LM if and only if one of the following holds: i) l = {(x,y)| x=a} (vertical line); ii) l = {(x,y)| y=b} (horizontal line) iii) ( = {(x,y)| y = mx +b where m<0} (line with negative slope) [ m(x - x0) if x xo when m>0}. (bent line W 14,9 m ( x - x0) if x > xo with...
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