Given
find where the line tangent to r at t=2 intersects the plane
through the three points (1,0,2), (-1,0,4), and (2,-1,1)
Given find where the line tangent to r at t=2 intersects the plane through the three points (1,0,2), (-1,0,4), and (2,...
intersects the plane Q3: Find the point where the line x x = + 2t , y = -2t, z = 1+t through P (1,1,-1). Q(2,0.2) and S (0,2,1) ?
Solve for 14(b,c) and 18 (b,c) please
16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the graph of r(t) (e.2 cos(t).2sin(t)) at to-0. Use the qu tion to approximate r(0.1). tion function to find the velocity and position vectors at t 2. 17. Find the principal unit normal vector to tih curve at the specified value of the parameter v(0)-0, r(0)-0 (b) a(t)cos(t)i - sin(t)i (a) r(t)-ti+Ij,t 2 (b) rt)-In(t)+(t+1)j.t2 14. Find the...
Q3. Find the unit tangent vector to the curve (t) t, 2,1 at the points where it cuts the plane 2x = z-y.
Q3. Find the unit tangent vector to the curve (t) t, 2,1 at the points where it cuts the plane 2x = z-y.
to the plane containing (-1,1,2), (9,2,0), and (3, 1,1) S2. Find the equation of the tangent plane to the graph of f(x,y)-sin(ry) at the point where r/3, y-1
to the plane containing (-1,1,2), (9,2,0), and (3, 1,1) S2. Find the equation of the tangent plane to the graph of f(x,y)-sin(ry) at the point where r/3, y-1
2) Find the points on the given curve where the tangent line is horizontal or vertical r3 cos (0)
a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize L. Find the point Q where L intersects the xy-plane. b) Find the angle that the line through (0,-1,1) and (√3,1,4) makes with a normal vector to the xy-plane. c) Find the distance from the point (3,1,-2) to the plane x-2y+z=4. d) Find a Cartesian equation for the plane containing (1,1,2), (2,1,1) and (1,2,1)
For the polar equation r= 1-sinθ a) Sketch the graph for 0 ≤ t ≤ 2pi b) Find the points on the cardioid where the tangent line is horizontal c)Find the equation of the tangent line when theta=pi/3
Find the point at which the line intersects the given plane. x = y – 2 = 4z; 4x – y + 2z = 12 (x, y, z) = ( (x, y, z) = D
Question 3. (15 pts) Given the function z = sin(ry) +2. Find the tangent plane equation at (1,0,2).
4. (4 pts) Consider the
surface z=x2y+y3.(a) Find the normal direction of the tangent plane
to the surface through (1,1,2).(b) Find the equation of the tangent
plane in (a).(c) Determine the value a so that the vector−→v=−−→i+
2−→j+a−→k is parallel to the tangent plane in (a).(d) Find the
equation of the tangent line to the level curve of the surface
through (1,1).
4. (4 pts) Consider the surface z = z2y + y). (a) Find the normal direction of the...