Explanation Given info: r → ( t ) = ( Sin t , Cos t , Sin t Cos 2 t ) Concept used: Point of intersection of r → ( t ) = ( Sin t , Cos t , Sin t Cos 2 t ) and x y plane is that point on the curve whose z co-ordinate becomes zero. Calculation: The point of intersection of r → ( t ) = ( Sin t , Cos t , Sin t Cos 2 t ) and x y plane is that point on the curve, whose, z component becomes zero. That is, Sin t . Cos 2 t = 0 Sin t = 0 and Cos2 t = 0 ( Sin θ = 0 ⇒ θ = n π , where n is integer Cos θ = 0 ⇒ θ = ( 2 n + 1 ) π 2 where n is integer ) t = n π , Where n is interger = ------ − 2 π , − π , 0 , π , 2 π , ----- 2 t = ( 2 n + 1 ) π 2 t = ( 2 n + 1 ) π 4 = ----- − 3 π 4 , − 3 π 4 , − π 4 , π 4 , 3 π 4 , ----- Co-ordinate of points on the curve periodic function, so after that all co-ordinate will repeat The values of t that lie between [ 0 , 2 π ] are 0 , π , 2 π , π 4 , 3 π 4 , 5 π 4 , 7 π 4 , Point corresponding to t = 0 ( Sin t , Cos t , Sin t . Cos 2 t ) = ( 0 , 1 , 0 ) Point correspondingto t = π ( Sin t , Cos t , Sin t . Cos 2 t ) = ( Sin π , Cos π , Sin π . Cos 2 π ) = ( 0 , − 1 , 0 ) Point correspondingto t = 2 π ( Sin t , Cos t , Sin t . Cos 2 t ) = ( Sin 2 π , Cos 2 π , Sin 2 π ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.1, Problem 27E

To determine

Find the points where $\vec{r} (t)$ intersects the $x y$ plane

$\vec{r} (t) = (Sin t, Cos t, Sin t Cos 2 t)$

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Chapter 14.1, Problem 26E

Chapter 14.1, Problem 28E

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Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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Find the points where r → ( t ) intersects the x y plane r → ( t ) = ( Sin t , Cos t , Sin t Cos 2 t )

Solution Summary: The author explains the point of intersection of r ( t ) and x y plane is that point on the curve whose z co-ordinate becomes zero.

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Find the points where $\vec{r} (t)$ intersects the $x y$ plane

$\vec{r} (t) = (Sin t, Cos t, Sin t Cos 2 t)$

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Chapter 14 Solutions

Find the points where r → ( t ) intersects the x y plane r → ( t ) = ( Sin t , Cos t , Sin t Cos 2 t )

Solution Summary: The author explains the point of intersection of r ( t ) and x y plane is that point on the curve whose z co-ordinate becomes zero.

Concept explainers

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Find the points where r→(t) intersects the xy plane r→(t)=(Sint, Cost,SintCos2t)

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Chapter 14 Solutions

Find the points where $\vec{r} (t)$ intersects the $x y$ plane

$\vec{r} (t) = (Sin t, Cos t, Sin t Cos 2 t)$