Explanation Given info. r → 1 ( t ) = ( 8 − t , 2 t , 3 t ) r → 2 ( t ) = t 3 i ∧ − 7 t 3 j ∧ + t 3 k ∧ r → 3 ( t ) = ( 8 − 4 t 3 − 2 + 5 t 2 + 9 t 3 ) Concept used: Parametric equation of line passing through r → 0 = ( x 0 y 0 , z 0 ) And parallel to vector V → is r → = r → 0 + t v → = ( x 0 y 0 , z 0 ) + t ( V x i ∧ + V y i ∧ + V z k ∧ ) = ( x 0 + t V x ) i ∧ + ( y 0 + t V y ) j ∧ + ( z 0 + t V z ) k ∧ = ( x 0 + t V x , y 0 + t V y , z 0 + t V z ) From above it becomes clear that same power should appear in x , y , z coordinate of parameter (t) then it represents equation of straight line in parametric form. Calculation: r → 1 ( t ) = ( 8 − t , 2 t , 3 t ) = ( 8 − t 1 , 2 t 1 , 3 t 1 ) All x , y and z coordinate are linear function of t so it represent equation of straight line

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.1, Problem 1PQ

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Which one of the following does not parameterize a line?

r→1(t)=(8−t,2t,3t)

r→2(t)=t3i∧−7t3j∧+t3k∧

r→3(t)=(8−4t3−2+5t2+9t3)

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Chapter 13, Problem 71CRE

Chapter 14.1, Problem 2PQ

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Question 4. Suppose you need to know an equation of the tangent plane to a surface S at the point P(2, 1, 3). You don't have an equation for S but you know that the curves r1(t) = (2 + 3t, 1 — t², 3 − 4t + t²) r2(u) = (1 + u², 2u³ − 1, 2u + 1) both lie on S. (a) Check that both r₁ and r2 pass through the point P. 1 (b) Give the expression of the 074 in two ways Ət ⚫ in terms of 32 and 33 using the chain rule მყ ⚫ in terms of t using the expression of z(t) in the curve r1 (c) Similarly, give the expression of the 22 in two ways Əz ди ⚫ in terms of oz and oz using the chain rule Əz მყ • in terms of u using the expression of z(u) in the curve r2 (d) Deduce the partial derivative 32 and 33 at the point P and the equation of მე მყ the tangent plane

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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Which one of the following does not parameterize a line? r → 1 ( t ) = ( 8 − t , 2 t , 3 t ) r → 2 ( t ) = t 3 i ∧ − 7 t 3 j ∧ + t 3 k ∧ r → 3 ( t ) = ( 8 − 4 t 3 − 2 + 5 t 2 + 9 t 3 )

Solution Summary: The author analyzes the parametric equations of a line passing through.

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Which one of the following does not parameterize a line?

r→1(t)=(8−t,2t,3t)

r→2(t)=t3i∧−7t3j∧+t3k∧

r→3(t)=(8−4t3−2+5t2+9t3)

Want to see the full answer?

Chapter 14 Solutions

Which one of the following does not parameterize a line? r → 1 ( t ) = ( 8 − t , 2 t , 3 t ) r → 2 ( t ) = t 3 i ∧ − 7 t 3 j ∧ + t 3 k ∧ r → 3 ( t ) = ( 8 − 4 t 3 − 2 + 5 t 2 + 9 t 3 )

Solution Summary: The author analyzes the parametric equations of a line passing through.

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Which one of the following does not parameterize a line? r→1(t)=(8−t,2t,3t) r→2(t)=t3i∧−7t3j∧+t3k∧ r→3(t)=(8−4t3−2+5t2+9t3)

Want to see the full answer?

Chapter 14 Solutions

Which one of the following does not parameterize a line?

r→1(t)=(8−t,2t,3t)

r→2(t)=t3i∧−7t3j∧+t3k∧

r→3(t)=(8−4t3−2+5t2+9t3)