1) Find an equation of the plane that passes through the point (8, 5, 1) and...

 

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1) Find an equation of the plane that passes through the point (8, 5, 1) and is parallel to the yz-plane. 2) Find a set of parametric equations of the line that passes through the point (1, 4, 5) and is parallel to v = 7i 4j. (x(), y(0), 2(0)) = 3) The position vector r describes the path of an object moving in space. Find the velocity, speed, and acceleration of the object.r(t) = 7ti + 2tj+6tk v(t) = s(t) = a(t) = 4) Use the given acceleration function to find the velocity and position vectors. Then find the position at time t = 9. a(t) = 8i + 4k, v(0) = 8j, r(0) = 0 v(t)=, r(t)=, r(9)= 5) Find the unit tangent vector to the curve at the specified value of the parameter. (Give your answers correct to 3 decimal places.) r(t) = i +3j, t=4 6) Find T(), N(t), ar, and an at the given time t for the curve r(). (Give your answers correct to 3 decimal places.) r(t) = i +5j, t=2 1) Find an equation of the plane that passes through the point (8, 5, 1) and is parallel to the yz-plane. 2) Find a set of parametric equations of the line that passes through the point (1, 4, 5) and is parallel to v = 7i 4j. (x(), y(0), 2(0)) = 3) The position vector r describes the path of an object moving in space. Find the velocity, speed, and acceleration of the object.r(t) = 7ti + 2tj+6tk v(t) = s(t) = a(t) = 4) Use the given acceleration function to find the velocity and position vectors. Then find the position at time t = 9. a(t) = 8i + 4k, v(0) = 8j, r(0) = 0 v(t)=, r(t)=, r(9)= 5) Find the unit tangent vector to the curve at the specified value of the parameter. (Give your answers correct to 3 decimal places.) r(t) = i +3j, t=4 6) Find T(), N(t), ar, and an at the given time t for the curve r(). (Give your answers correct to 3 decimal places.) r(t) = i +5j, t=2