Explanation Given info: r 1 → ( + ) = ( t 2 + 3 , t + 1 , 6 t − 1 ) r → 2 ( t ) = ( 4 t , 2 t − 2 , t 2 − 7 ) 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. t 2 + 3 = 4 t → ( i ) t + 1 = 2 t − 2 → ( i i ) 6 t = t 2 − 7 → ( i i i ) Solving equation ( i ) t 2 + 3 = 4 t t 2 − 4 t + 3 = 0 Spiting middle term t 2 − 3 t − t + 3 = 0 t ( t − 3 ) − 1 ( t − 3 ) = 0 ( t − 1 ) ( t − 3 ) = 0 ( t − 1 ) ( t − 3 ) = 0 t = 1 and 3 . Solving equation ( i i ) t + 1 = 2 t − 2 t = + 1 + 2 t = 3. Checking t = 1 or t = 3 does not satisfy equation ( i i i ) 6 t = t 2 − 7. Checking for t = 1 6 1 ≠ ( 1 ) 2 − 7 6 1 ≠ − 6 Hence t = 1 does not satisfies. Checking for t = 3. L . H . S = 6 t = 6 3 = 2 R . H . S = ( 3 ) 2 − 7 = 9 − 7 = 2 Hence t = 3 satisfy. So at t = 3 r 1 → ( + ) and r 2 → ( + ) collide. Collision point ( 4 t , 2 t − 2 , t 2 − 7 ) ( Putting the value of t = 3 ) = ( 4.3 , 2.3 − 2 , ( 3 ) 2 − 7 ) = ( 12 , 4 , 2 ) r 1 → ( + ) and r 2 → ( + ) Intersect if r 1 → ( + ) = r 2 → ( S ) r 1 → ( + ) = r 2 → ( S ) t 2 + 3 = 4 s → ( i ) t + 1 = 2 S − 2 → ( i i ) 6 t − 1 = S 2 − 7 → ( i i i ) Putting the value of S form ( i ) in ( i i ) t 2 + 3 4 = S Put this S value in ( i i ) t + 1 = 2 ( t 2 + 3 4 ) − 2...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Videos

Question

Chapter 14.1, Problem 37E

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.

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.1, Problem 36E

Chapter 14.1, Problem 38E

Students have asked these similar questions

Consider the graphs of y = f(x) and y = g(x) in the given diagram y= f(x). y = g(x) Evaluate (f+g)(2) -5 Determine all for which g(x) < f(x) Determine all for which f(x) +3 = g(x)

I) For what value(s) of x does g(x) = -4? Separate multiple answers with commas as needed. J) Give the interval(s) of such that g(x) > 0. Use the union symbol between multiple intervals. K) Give the interval(s) of such that g(x) <0. Use the union symbol between multiple intervals.

need help on B

Chapter 14 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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 2 + 3 , t + 1 , 6 t − 1 ) r → 2 ( t ) = ( 4 t , 2 t − 2 , t 2 − 7 )

Solution Summary: The author calculates the coordinates of r 1 ( t ) and the corresponding point if they exist.

Videos

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

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

Want to see the full answer?

Chapter 14 Solutions

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 2 + 3 , t + 1 , 6 t − 1 ) r → 2 ( t ) = ( 4 t , 2 t − 2 , t 2 − 7 )

Solution Summary: The author calculates the coordinates of r 1 ( t ) and the corresponding point if they exist.

Videos

Determine whether r1→(t) and r2→(t) collide or intersect giving the coordinates of the corresponding point if they exist. r1→(t)=(t2+3,t+1,6t−1)r→2(t)=(4t,2t−2,t2−7)

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.

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