Let 7 (t) = (3t2 – 1,t? – 2t3, Find the line (L) tangent to r(t) at the point (11, – 12, – 64) – 4t4). L:(r, y, z) +t

Q: Let r(t) (t¹ + 4, t² + 2t¹, − 4t³). Find the line (L) tangent to r(t) at the point (20, 36, 32) = L:…

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Q: a. Find a function (f(x,y,z)) such that (F = Vf(x,y,z))? b. Use part (a) to evaluate (F. dr ) along…

A: We have to evaluate the ∫CF.→dr→.

Q: Let 7(t) = (- 2t³ – 3, t2 + t, - 4t2). Find the line (L) tangent to 7 (t) at the point (- 19, 12, –…

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Q: nd the tangent plane to the equation z = a? – 4y? – 2y at the point ( – 3, 3, – 33)

A: In this question, concept of tangent  is used. Tangent A tangent is the line that runs parallel to…

Q: Find the line (L) tangent to r(t) at t = -1. L: (x, y, z) = +t

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Q: Find the length of the line given by r(t) = ⟨t, 2t⟩, for a ≤ t ≤ b.

A: To determine: The length of the line given by rt=<t,2t> for a≤t≤b

Q: Find the points on the curve x = £² – 4t − 6, y = t² + 10€ that have: : A. a horizontal tangent line…

A: Let us consider the given curve x(t),y(t). The horizontal tangent line is obtained as dydt=0 The…

Q: Find the speed of the object whose position function is given by 7(t) = (6t + 5, 3t + 6, t³ + 4t) at…

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Q: Find the intersection of the plane x - X = y = - 4y - 5z = -137 and the line r(t) = (5, −5, −4)t +…

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Q: Find the point at which the line r(t) y(t) z(t) = -6-7t 7+t - 54t intersects the z plane.

A: Let's find intersect points.

Q: Let F(t) = (-3t² - 1, t³ – 5tª, – 3t²). Find the line (L) tangent to r(t) at the point (-4,-4, − 3)…

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Q: Let (t)=(-5t2+4,t³-+4,2+³) 7 Find the line (L) tangent to (t) at the point (-1,0,2) L: (x,y,₁2)= +t

A: The given problem is to find the line tangent to the given parametric curve at the given point…

Q: Find the speed of the curve 7 (t) = (5t2 + + 6, 7t + 1, t³ + 8t) at t = 4 Бpeed

A: Magnitude of the velocity is speed

Q: Find the length of the curve r(t) (1,t²,), 0sts1 %3D «3 Ost<1

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Q: If f(x, y)= xe2y +y, evaluate grad f •dr where C is the straight line joining the point (2,0) to the…

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Q: = (1, -2,2) FIND: The distance from B to the line, L. d(B, L). B b = AB B = b OA = Ĉ(0) = (1, 2, 1)…

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Q: Let r(t) = (-5t³ – 1, t² + 5t³, 3t²). Find the line (L) tangent to (t) at the point (39, -36, 12)

A: r→(t)=⟨−5t3−1,t2+5t3,3t2⟩Find the line (L) tangent to r→(t) at the point (39,−36,12)