2. [-I2 Points] DETAILS LARCALC1O 11.5.005. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find sets of parametric equations and symmetric equations of the line through the point parallel to the given vector or line (if possible). Point Parallel to (5,0,4) v=4i+5j3k (a) parametric equations (Enter your answers as a commaseparated list.) (b) symmetric equations 3. [-I2 Points] DETAILS LARCALC1O 11.5.008. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find sets of parametric equations and symmetric equations of the line through the point parallel to the given vector or line (if possible). Point Parallel to (3.6,5) *;1 =_L31=Z5 (a) parametric equations (Enter your answers as a comma-separated list.) (b) symmetric equations 0 X - 2 = L = z 5 3 X-3 =L6_z 2 3 OX+3 =L3=z+5 2 6 0X23 =L35=Z_5 Need Help? _m . [16 Points] DETAILS LARCALCET7 12.3.004. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = ti + (t2 + 9)j (1, 8) (a) Find the velocity vector v(t), speed 5(t), and acceleration vector a(t) of the object. V('-\") = 50:) = a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point. : 3(1) = (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point. Y Y 10 HNWDL'IOQN HNWODUIQN'\" Need Help? . [I3 Points] DETAILS LARCALCET7 12.3.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the given acceleration function and initial conditions to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 5. a(t) = 4i + 2k v(0) = 8j, r(0) = 0 v(t) = M) = r(5) = Need Help? _'' UUU . [I5 Points] DETAILS LARCALCET7 12.3.014. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The position vector r describes the path of an object moving in space. Position Vector Time r(t)=3ti+tj+%t2k t=4 (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. V(f) = s(t) = a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given value oft. 3(4) = Need Help? 5. {-11 Points] DETAILS LARCALC1O 11.5.038. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of the plane passing through the point perpendicular to the given vector or line. Point Perpendicular to (0, 8, 0) n = 5i + 6k 6. [-I1 Points] DETAILS LARCALCET7 11.5.048. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of the plane with the given characteristics. The plane passes through the point (5, 9, 9) and is parallel to the yz-plane. Z Need Help? _ . [I6 Points] DETAILS LARCALCET7 12.3.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 4 cos ti + 4 sin ti (2x/3, 2x5) (a) Find the velocity vector v(t), speed 5(t), and acceleration vector a(t) of the object. v(t) = 50:) = a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point. 4%) = j : Need Help