#3 only! 3.) (5 Points) Consider the vector-valued function , where f(t) = ha co
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#3 only!
3.) (5 Points) Consider the vector-valued function , where f(t) = ha cos ?t, b sin ?t, c t + 1i and a, b, c, ? ? R are positive constants.
(a) Determine the derivative f 0 (t).
(b)Find a vector parametrization of the tangent line to the path described by f at the point with position vector (a, 0, 1).
Topic: Written Assignmen x/ D written-hw1.pdf .g search Q&A; | Chegg.com D Calculus lll-Equations of Dot Product and Normal × × × Cfile:///C:/Users/Matt/Downloads/written-hw1.pdf -Rogawski, Calculus: E c) Find an equation of the plane through the point D Login-OpenStack D 1,2, 3) that is parallel to the ::: Apps Canvas is Here Univ KissAnime Watch a UK MA 114 Common Co Homepage of Unive Virtual Machine vectors u and w (2) (5 Points) Consider the plane P in R3 with equation 2a 3y +4z-12 and the point P-3-4. 7) (a) Let L be the line through the point P that is orthogonal to the plane P. Determine the point Q, where the plane P intersects the line L (b) Find the distance between the point P and the plane P (3) (5 Points) Consider the vector-valued function f : R R3, where f(t) = (a cos at, bsinat, ct + 1 and a,b,c, w E R are positive constants. (a) Determine the derivative f'(t) (b) Find a vector parametrization of the tangent line to the path described by f at the point with position vector a, 0, 1 4:08 PM 9/15/2016Explanation / Answer
f(t) = < a.cos( t ) , b.sin( t ) , ct + 1 >
f'(t) = < -a.sin( t ) , b.cos( t ) , c >
We need to calculate the tangent equation at < a , 0 , 1 > => t = 0
=> f'(0) = < 0 , b , c >
Equation of tangent
( 0 )*( x - a ) + ( b )*( y - 0 ) + ( c )*( z - 1 ) = 0
( b )y + ( c )z = c
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