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...

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Chapter 14.1, Problem 38E

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

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

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Chapter 14.1, Problem 37E

Chapter 14.1, Problem 39E

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

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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 )

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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)

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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.

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