![(2 marks) 24. By analyzing the normals, determine if the three planes intersect in a point. 찌 x-Sy+2-10-0 π2 [x,y,2]-[0, 0,](http://img.homeworklib.com/images/5d933342-2aed-4752-9c21-c8ab09f62547.png?x-oss-process=image/resize,w_560)
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(2 marks) 24. By analyzing the normals, determine if the three planes intersect in a point. 찌 x-Sy+2-10-0 π2'...
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25....
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x, y, z] = [2,-2, 0] + r[2 kx+Zy-4: = 12. -3] is parallel to the plane (2 marks)
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x,...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent p...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
7. Three planes can intersect in a number of different ways. For each of the combinations...
7. Three planes can intersect in a number of different ways. For each of the combinations below, find the single point of intersection if there is one. If there isn't, explain how the planes do intersect. 71: 67 + 2+ 3z – 9 = 0 a. 12: -2x - 5y + 32 - 4 = 0 7T3 : 5x – y + 2z + 3 0 2x – 3y + 5z – 2 = 0 b. 72: -5.0 + 2y...
Matching: Match the equation of each plane to its scalar form 2x-y-2-6.0 b.y Answer Alternate Equation 17 [x, y, :1...
Matching: Match the equation of each plane to its scalar form 2x-y-2-6.0 b.y Answer Alternate Equation 17 [x, y, :1 = [3, 2, 1]+42. 0, 31+13.0,2]s,t ER. 18. [x,y,:] = [5.-2. 31+43.-2.4]여5.-2, 6] s, t E R. 19. -1+2+3 20. [x,y,s]-[5, 4,-2]+42,-1,-1] 1.3.3]stER. 21. x--t + 22 y-2-1+4s s,tER. 22. Find the values of k such that the three planes never intersect in a point. (3 marks 4x+y- 17- x-y-kz+11-0 Page 3 of 6 23. The equation of a plane...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2b with b ER. (a) Prove that the tangent line of each curve in H at a point (r, y) with y / 0 has slope (b) Let y -f(x) be a...
3. Find the point(s) of intersection for the following three planes. Ty : x - y...
3. Find the point(s) of intersection for the following three planes. Ty : x - y +z = 0 T2: x + 2y – Z-8= 0 Tz: 2x - 2y +z+11=0
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y =...
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y = 5 + 2t, z=t-1 and 1 1 - 2 L2 : =y-3 = 2 4 i. Check whether the lines Lị and L2 parallel, intersect or skewed? (5 marks) ii. Find the shortest distance from the point (1, 2, -1) to the line Li- (3 marks) b) Given two planes 71 : 20 - 4y +z = 5 and T2 : 7x + y...
vectors. Need help with those questions please 1a). In three-space, find the intersection point of the...
vectors. Need help with those questions please
1a). In three-space, find the intersection point of the two lines: (x, y, z) = (-1,2,0] + [3,-1, 4) and [x, y, ) = -6, 8, -1] + [2,-5, -3). b) Determine a direction vector in integer form of the line of intersection of the two planes 2x + 2y+2-12-0 and (x, y, z)=(2,0,0]+${1,2,0]+(1.0,-2) [2,3] 2. What is the distance between the point (-81) and the plane 5x-2-2y+52 [2] 3. Find the point(s)...
hlep me these 2 t, 3- 3 and (-2r, 3-, ) 11.) Determine the point of...
hlep me these
2 t, 3- 3 and (-2r, 3-, ) 11.) Determine the point of intersection of the lines Note:4,1,2, with (1,2/3,-1)^k(-2.-1,1)=kv;, for any kER. So .1,. Change one of the parameters to s, then equate the corresponding coordinates of the lines and solve for t, and s. substitute the values of t, and s in their respective lines to get the required point. Locate the point of intersection of the plane 2x+ y-z-0 and the line through (3,1,0)...
4. For this question, we define the following matrices: 1-2 0 To 61 C= 0 -1...
4. For this question, we define the following matrices: 1-2 0 To 61 C= 0 -1 2 , D= 3 1 . [3 24 L-2 -1] (a) For each of the following, state whether or not the expression can be evaluated. If it can be, evaluate it. If it cannot be, explain why. i. B? +D ii. AD iii. C + DB iv. CT-C (b) Find three distinct vectors X1, X2, X3 such that Bx; = 0 for i =...
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x, y, z] = [2,-2, 0] + r[2 kx+Zy-4: = 12. -3] is parallel to the plane (2 marks)
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x,...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
7. Three planes can intersect in a number of different ways. For each of the combinations below, find the single point of intersection if there is one. If there isn't, explain how the planes do intersect. 71: 67 + 2+ 3z – 9 = 0 a. 12: -2x - 5y + 32 - 4 = 0 7T3 : 5x – y + 2z + 3 0 2x – 3y + 5z – 2 = 0 b. 72: -5.0 + 2y...
Matching: Match the equation of each plane to its scalar form 2x-y-2-6.0 b.y Answer Alternate Equation 17 [x, y, :1 = [3, 2, 1]+42. 0, 31+13.0,2]s,t ER. 18. [x,y,:] = [5.-2. 31+43.-2.4]여5.-2, 6] s, t E R. 19. -1+2+3 20. [x,y,s]-[5, 4,-2]+42,-1,-1] 1.3.3]stER. 21. x--t + 22 y-2-1+4s s,tER. 22. Find the values of k such that the three planes never intersect in a point. (3 marks 4x+y- 17- x-y-kz+11-0 Page 3 of 6 23. The equation of a plane...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2b with b ER. (a) Prove that the tangent line of each curve in H at a point (r, y) with y / 0 has slope (b) Let y -f(x) be a...
3. Find the point(s) of intersection for the following three planes. Ty : x - y +z = 0 T2: x + 2y – Z-8= 0 Tz: 2x - 2y +z+11=0
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y = 5 + 2t, z=t-1 and 1 1 - 2 L2 : =y-3 = 2 4 i. Check whether the lines Lị and L2 parallel, intersect or skewed? (5 marks) ii. Find the shortest distance from the point (1, 2, -1) to the line Li- (3 marks) b) Given two planes 71 : 20 - 4y +z = 5 and T2 : 7x + y...
vectors. Need help with those questions please
1a). In three-space, find the intersection point of the two lines: (x, y, z) = (-1,2,0] + [3,-1, 4) and [x, y, ) = -6, 8, -1] + [2,-5, -3). b) Determine a direction vector in integer form of the line of intersection of the two planes 2x + 2y+2-12-0 and (x, y, z)=(2,0,0]+${1,2,0]+(1.0,-2) [2,3] 2. What is the distance between the point (-81) and the plane 5x-2-2y+52 [2] 3. Find the point(s)...
hlep me these
2 t, 3- 3 and (-2r, 3-, ) 11.) Determine the point of intersection of the lines Note:4,1,2, with (1,2/3,-1)^k(-2.-1,1)=kv;, for any kER. So .1,. Change one of the parameters to s, then equate the corresponding coordinates of the lines and solve for t, and s. substitute the values of t, and s in their respective lines to get the required point. Locate the point of intersection of the plane 2x+ y-z-0 and the line through (3,1,0)...
4. For this question, we define the following matrices: 1-2 0 To 61 C= 0 -1 2 , D= 3 1 . [3 24 L-2 -1] (a) For each of the following, state whether or not the expression can be evaluated. If it can be, evaluate it. If it cannot be, explain why. i. B? +D ii. AD iii. C + DB iv. CT-C (b) Find three distinct vectors X1, X2, X3 such that Bx; = 0 for i =...
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