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Vequations of (d). Find the result of a). 29 1° Show that the vectors u (1; 2; 1) and v (3; 6; 2) are not collinear. 2° Determine the coordinates of a non-zero vector w and distinct from u and v , such that u, v and w coplanar. 3° Show that the points A (1 ;0; 2), B (1 ; 1;0) and C(2,2,-1) are not collinear. Then wri. system of parametric equations of the plane(ABC). A.B, C and D are coplanar

Vequations of (d). Find the result of a). 29 1° Show that the vectors u (1; 2; 1) and v (3; 6; 2) are not collinear. 2° Determine the coordinates of a non-zero vector w and distinct from u and v , such that u, v and w coplanar. 3° Show that the points A (1 ;0; 2), B (1 ; 1;0) and C(2,2,-1) are not collinear. Then wri. system of parametric equations of the plane(ABC). A.B, C and D are coplanar

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 97E
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ATAL Pm MOUS To go furller 28 Consider (O : OA , OB ,OC ) an orthonormal system in space. Let G be the center of gravity of angle ABC. C\ co Calculate the coordinates of G. ABCDEFGH is a cube. The space is referred to a direct orthonormal system (A; AB ,AD ,AE). 2° Consider the points A' (2;0; 0), B' (0 ; 2; 0) and C' (0 ; 0 ; 3). E a Verify that these three points define a plane. non-colliner 1,J, K and L are points defined as: Write a system of parametric equations of the plane (A'B'C'). DC ,BJ = 4. 39 Write a system of parametric equations of line (AC). 1° Find the coordinate of all points in this 4° Verify that K (4; 0-3) is the trace of the line (AC) with the plane (A'B'C'). figure. 50 5 Verify that line (BC) cuts the plane (A'BC'/at L (0; 4 ;-3). 6 Verify that (AB), (A'B') and (KL) are parallel. 2° Show that K lies in plane (EGJ) . b Determine the intersection (d) of the two planes (ABC) and (A'B'C'). Write a system of parametric equations of (d). Find the result of a). 3° a) Show that EKIH is a parallelogram. b) Deduce that (HI) is parallel to plane (EGJ) . 29 1° Show that the vectors u (1 ; 2; 1) and v (3 ; 6; 2) are not collinear. 2° Determine the coordinates of a non-zero vector w and distinct from u and v , such that u, v and w are 4° Given the point M coplanar. Show that M is on line (IG) for all a. 3° Show that the points A (1;0; 2), B (1;i;0) and C (2,2,-1) are not collinear. Then write a system of parametric equations of the plane(ABC). 5° Find the coordinates of K in the system (C ; 4° Find the coordinates of point D distinct from A , B and C such that A, B,C and D are coplanar. 294 plane: coplanar
Transcribed Image Text:ATAL Pm MOUS To go furller 28 Consider (O : OA , OB ,OC ) an orthonormal system in space. Let G be the center of gravity of angle ABC. C\ co Calculate the coordinates of G. ABCDEFGH is a cube. The space is referred to a direct orthonormal system (A; AB ,AD ,AE). 2° Consider the points A' (2;0; 0), B' (0 ; 2; 0) and C' (0 ; 0 ; 3). E a Verify that these three points define a plane. non-colliner 1,J, K and L are points defined as: Write a system of parametric equations of the plane (A'B'C'). DC ,BJ = 4. 39 Write a system of parametric equations of line (AC). 1° Find the coordinate of all points in this 4° Verify that K (4; 0-3) is the trace of the line (AC) with the plane (A'B'C'). figure. 50 5 Verify that line (BC) cuts the plane (A'BC'/at L (0; 4 ;-3). 6 Verify that (AB), (A'B') and (KL) are parallel. 2° Show that K lies in plane (EGJ) . b Determine the intersection (d) of the two planes (ABC) and (A'B'C'). Write a system of parametric equations of (d). Find the result of a). 3° a) Show that EKIH is a parallelogram. b) Deduce that (HI) is parallel to plane (EGJ) . 29 1° Show that the vectors u (1 ; 2; 1) and v (3 ; 6; 2) are not collinear. 2° Determine the coordinates of a non-zero vector w and distinct from u and v , such that u, v and w are 4° Given the point M coplanar. Show that M is on line (IG) for all a. 3° Show that the points A (1;0; 2), B (1;i;0) and C (2,2,-1) are not collinear. Then write a system of parametric equations of the plane(ABC). 5° Find the coordinates of K in the system (C ; 4° Find the coordinates of point D distinct from A , B and C such that A, B,C and D are coplanar. 294 plane: coplanar
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