answer q5,6,7,8 please Find the unit tangent vector T(0) at the point with the gliven value of the parameter t. r(t)...
please answer both
(12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0
(12(8 pts) Find parametric equations of the line through the point (2,...
(a) Find the unit tangent vector, T(t) and the unit normal vector, N(t), for the space curve r(t) cos(4t), sin(4t), 3t >. (b) From part (a), show that T(t) and N(t) are orthogonal
(a) Find the unit tangent vector, T(t) and the unit normal vector, N(t), for the space curve r(t) cos(4t), sin(4t), 3t >. (b) From part (a), show that T(t) and N(t) are orthogonal
Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = (2 – 3t, 1 + 4t, 582 + 2x2), t = 4 T(4) = <5,4,720 > 720.02847 x
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y + sin(40k. (b) Find the unit tangent vector at the point t0. SOLUTION (a) According to this theorem, we differentiate each component of r: t 45 cos (4t) r(t) + 3 (b) Since r(0)= and r(o) j+4k, the unit tangent vector at the point (3, 0, 0) is i+ 4k T(0) = L'(0)--
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y +...
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...
Question 9 Let r(t)={cos 2t, sin 2t, V5t) a) Find the unit tangent vector and the unit normal vector of r(t) at += TI (Round to 2 decimal places) TE)= NG) = < b) Find the binormal vector of r(t) at t = TT 2 (Round to 2 decimal places) BC) =< A Moving to another question will save this response.
Find the derivative, r'(t), of the vector function. r(t) = eti- j+ln(1 + 7t)k r'(t) = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. T = 5e, y = te, c = tetp:/5, 0, 0) x(t), y(t), z(t) =
12.1.24 Question Help The tangent line to a smooth curve r(t) = f()i + 96)j + h(t]k at t= to is the line that passes through the point (f(t):(to)."(to) parallel to (to)the curve's velocity vector at to User (to) and (t) to find parametric equations for the line that is tangent to the given curve at the given parameter value t= to (1)-(31²)i + (4 + 3)j + (52) 10-3 What is the standard parametrization for the tangent line? yo...
(1 point) Consider the helix r(t)-(cos(-4t), sin (-4t), 4t). Compute, at t A. The unit tangent vector T-( B. The unit normal vector N -( C. The unit binormal vector B( D. The curvature K = Note that all of your answers should be numbers
(1 point) Consider the helix r(t)-(cos(-4t), sin (-4t), 4t). Compute, at t A. The unit tangent vector T-( B. The unit normal vector N -( C. The unit binormal vector B( D. The curvature K...
Suppose the vector-valued function rt-tht) is smooth on an interval containing the point t -to is the line parallel to the tangent vector r()that passes through ()().()).For the following function, find the line tangent to the curve at t to the point to The line tangent to r(t) at r(t) (10 cos t,6 sin 16t,t), to Theline tangent to the curve at t:68COD
Suppose the vector-valued function rt-tht) is smooth on an interval containing the point t -to is the...