Please help me answer these questions

V QUESTION 11.3 Checking contact state. Choose one . 5 points what is the collision state of a body moving with velocity u = (3,1, -3)m/s with respect to a plane with normal vector n = (2, 3, 3) assuming the body is above the plane. O Colliding contact O Separation contact O Resting contact O None of the aboveQUESTION 1 Quadratic Equation Choose one . 5 points 1. Solve c'+ 41 -5 =0 using the quadratic formula O m1 = 1, 12 = -5 O I= 1, 12 =5 O I1 = -1, 12 = -5QUESTION 10.2 Finding a Sphere Center and Radius Choose one . 5 points Find the center c and radius r of the sphere S: (x + 1)2 + (y -2)2+ (z -2)? =4 d= (-1, 2, 2), T = 2 O = (-1, 2, 2), T = 4 = (1, -2, -2), T = 2 QUESTION 103 Writing the Equation of a Sphere Given its Center and Radius Choose one . 5 points Write the equation of a sphere with center c = (2,1, -5) and radius R = 3 O (I -2)2 + (y -1)2 + (2 +5)2 -9 O (z - 2)2 + (y - 1)2 + (2+5)2 -3 O ( +2)2 + (y + 1)2 + (2-5)2-9QUESTION 10.4 Writing the Equation of a Sphere Given its Center and Radius Choose one . 5 points Write the equation of a sphere with center c = (3, 2, 1) and radius R = 5 (c - 3)2 + (y -2)2 + (2 -1)2 = 25 O (x - 3)2 + (y -2) + (2 -1)2 =5 O (c + 3)2 + (y + 2)2+ (z+ 1)2 = 5GROUP 10 Sphere Equation Group . 4 questions A sphere is the set of points p = (I, y, 2)in 30 space that have a constant distance called the radius R with a fixed point c = (a, b, c) defined as the sphere center. The sphere algebraic equation is : (x - a) + (y - b) + (z-c)? = R2 where a, b, c are the components of the center c QUESTION 10.1 Finding a Sphere Center and Radius Choose one . 5 points Find the center c and radius r of the sphere S: (x + 7)2 + (y -4)2+ (z+9)2 =36 O Z = (7, -4, 9), T = 6 O C = (-7, 4, -9), T = 6 O E= (7, -4,9), T = 36QUESTION 11.2 Checking contact state. Choose one . 5 points what is the collision state of a body moving with velocity v = (1, 2, 4)m/s with respect to a plane with normal vector n = (1, 1, 0) assuming the body is above the plane. O Colliding contact O Separation contact O Resting contact O None of the aboveQUESTION 11.1 Checking contact state. Choose one . 5 points what is the collision state of a body moving with velocity v = (2, -3, 1)m/s with respect to a plane with normal vector n = (0, 1, 0) assuming the body is above the plane. O Colliding contact O Separation contact O Resting contact O None of the aboveQUESTION 12.2 Finding Second Sphere center and Radius Choose one . 5 points Find the center c2 and radius R, of sphere S2 O C2 = (-5, -5, -3) , R2 =4 O C2 = (-5,5, -3) , R2 = 2 O G = (5,5, 3) , R2 = 2 QUESTION 12.3 Find the Distance between the two Spheres Choose one . 5 points Calculate the distance | cic2 between the two sphere positions C102 - 25 CIC2 = 5 C102 =1QUESTION 12.4 Collision between two Sphers Choose one . 5 points Is there any collision between the 2 spheres ? O collision, C102 Ri + R2 O None of the aboveGROUP 12 Sphere-Sphere Collision Group . 4 questions Given the two spheres : S1 : (x - 1)2 + (y - 2)2 + (z -3)2 -9 and S2 : (x -5)2 + (y-5)2 + (z -3)2 =4 Answer the 4 questions below QUESTION 12.1 Find First Sphere center and radius Choose one . 5 points Find the center c and radius R, of sphere S, O Ci = (1,2, 3) , R1 = 3 O ci = (-1, -2, -3) , R1 = 3 O C = (-1, -2,3) , R1 =9QUESTION 2 Global Rotation Choose one . 5 points Write the global rotation matrix of 60 about the world I - aris , R.(60) O 0 1 /3 2 V3 O 0 V3 O O 0 0 V3 V3QUESTION 3 Global Rotation Choose one . 5 points Write the global rotation matrix of 450 about the world y-axis , R,(45) O V/2 2 1 V2 V2 2 O 0 V2 0 O 0 1 0 V2 0 2V QUESTION 4 Local Rotation Choose one . 5 points Write the local rotation matrix of 30 about the local Y-axis , BRY(30) O V3 0 2 1 0 0 V3 2 O V3 0 VE O VE 0 0 0QUESTION 5 Local Rotation Choose one . 5 points Write the local rotation matrix of 90 about the local Z-axis , #Rz(90) O 0 1 0 0 0 0 O 0 0 0 O 0 0 0 0 1QUESTION 6 Transforming a Vector from Local Space to World Space Choose one . 5 points A vector coordinate in body frame coordinate (rigid body) is ro = (4, 5, 3) ,calculate the vector coordinate in world space ~ if the orientation of the rigid body is 90 about the local X-axis. Note : T = R - To 2 O -3 on 09QUESTION 7 Transforming a Vector from World Space to Local Space Choose one . 5 points A vector coordinate in world space is F = (1, 0, 2) ,calculate the vector coordinate in body frame coordinate (rigid body) ro if the orientation of the rigid body is 90 about the global z-axis. Note: use To = R - r O O -1 2QUESTION 8 Transforming a Point from Local Space to World Space Choose one . 5 points A box is located at c = (2,1, 0) with orientation of 90 degree about the global x-axis. Calculate the position Pworld of a point in world space if the point coordinate in local space is Plocal-(4,0,2). Note : use Pworld = C+ R - To 6 -1 O 6 O NOPQUESTION 9 Transforming a Point from World Space to Local Space . Choose one . 5 points A box is located at c = (1, 1, 0) with orientation of 90 degree about the global z-axis. Calculate the position Plocal of a point in in local space if the point coordinate in world space is Pworld = (3, 4, 6) Note : Use Plocal = Rt - (Pworld - c) -3 O 3 -2 O