Explanation Given info: r 1 → ( t ) = ( t , t 2 , t 3 ) r → 2 ( t ) = ( 4 t + 6 , 4 t 2 , 7 − t ) Concept used: Two paths r 1 → ( t ) and r 2 → ( t ) intersect if there is a point p lying on both curves. We say that r 1 → ( t ) and r 2 → ( t ) collide if r 1 → ( t o ) = r 2 → ( t o ) at same time to. Calculation: r 1 → ( t ) and r 2 → ( t ) Collide if r 1 → ( t o ) = r 2 → ( t o ) at same time to. i . e Same x , y , and z coordinate exist for same value of parameter .so t = 4 t + 6 → ( A ) t 2 = 4 t 2 → ( B ) t 3 = 7 − t → ( C ) Solving equation ( A ) for t 4 t 2 − t 2 = 0 3 t 2 = 0 t = 0 From the solution of equation ( A ) and ( B ) you get there is no common value of t , so r 1 → ( t ) and r 2 → ( t ) Interact if r 1 → ( t ) = r 2 → ( S ) t = 4 S + 6 → ( D ) t 2 = 4 S 2 → ( E ) t 3 = 7 − S → ( F ) Putting value of S form ( D ) in ( E ) 4 S = t − 6 S = t − 6 4 t 2 = 4 ( t − 6 4 ) 2 t 2 = ( t − 6 4 ) 2 4 t 2 = ( t − 6 ) 2 4 t 2 = t 2 + 36 − 12 t 3 t 2 + 12 t − 36 = 0 Taking 3 as common 3 ( t 2 + 4 t − 12 ) = 0 t 2 + 4 t − 12 = 0 Spitting the middle term t 2 + 6 t − 2 t = 0 t ( t + 6 ) − 2 ( t + 6 ) = 0 ( t − 2 ) ( t + 6 ) = 0 t = 2 or − 6...

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Videos

Question

Chapter 14.1, Problem 38E

To determine

Determine whether $\vec{r_{1}} (t) and \vec{r_{2}} (t)$ collide or intersect giving the coordinates of the corresponding point if they exist.

$\begin{array}{l} \vec{r_{1}} (t) = (t, t^{2}, t^{3}) \\ {\vec{r}}_{2} (t) = (4 t + 6, 4 t^{2}, 7 - t) \end{array}$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.1, Problem 37E

Chapter 14.1, Problem 39E

Students have asked these similar questions

help on this question about Laplace transformation?

Help me expand this fraction below.

determine the final and initial value of the expression below: Help

Chapter 14 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Determine whether r 1 → ( t ) and r 2 → ( t ) collide or intersect giving the coordinates of the corresponding point if they exist. r 1 → ( t ) = ( t , t 2 , t 3 ) r → 2 ( t ) = ( 4 t + 6 , 4 t 2 , 7 − t )

Videos

Determine whether r1→(t) and r2→(t) collide or intersect giving the coordinates of the corresponding point if they exist. r1→(t)=(t,t2,t3)r→2(t)=(4t+6,4t2,7−t)

Want to see the full answer?

Chapter 14 Solutions

Determine whether $\vec{r_{1}} (t) and \vec{r_{2}} (t)$ collide or intersect giving the coordinates of the corresponding point if they exist.

$\begin{array}{l} \vec{r_{1}} (t) = (t, t^{2}, t^{3}) \\ {\vec{r}}_{2} (t) = (4 t + 6, 4 t^{2}, 7 - t) \end{array}$