Q3 – A// If P(1,2,-1),Q(2,-1,1), R(-1,-1,2) are three point in space. 1- Find the vector perpendicular to a plane contains PQ,PR. 2- Find the unit vector in the direction of PQ, PR. B// Evaluate the following integral : f cos(x) * six² (1) dx

Q: Define two vector functions F(t) = 8 sin(t)i + 6 cos(t)j + (t – 2)k ü(t) = 6 sin(t)i + 8cos(t)j + (t…

A: We have to find the dot product of r(t) and u(t)

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Q: 1. Let ř(1) = . Find a vector and parametric equation of the line tangent to F(1) at the point (-…

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Q: (a) F(t)=(2 sint)i + (2 cost)j from the point A(2, 0) to the point B(-2, 0)

A: To find the arc length of given function

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Q: Q1:- Find the domain of the following vector functions:- (a) f(t) = (cos nt)i – Ln(t)j + vt – 2k %3D

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Q: Find the positive t when the vector r(t) = (4t, 4t, 5t2 – 6) is perpendicular to r' (t). t =

A: We use the definition of the perpendicular of two vectors to find the positive value of t.

Q: f(x, y, z) = sin(ry + z) foksiyonunun| P(1, 7/4, 7/2) noktasinda v = -2i + j+ 2k

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Q: sider the vector-valued function R(t) with Ả(1) = (1,2,−1) and Ř'(t) = = 1 2 (²²/7/7 - 2) - Find…

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Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: 2) Let two vector functions be defined by r₁(t) = (2t, t², t²) r₂(t) = (sint, sin(3t),5t) a. Find…

A: a. Consider the given vector functions, r1(t)=2t,t2,t4r2(t)=sint,sin3t,5t if two vector function…

Q: Consider the function f(x,y) = 3- a. Fill in the table with the values of the directional derivative…

A: Here to find the directional derivative at (a, b) of fin(x, y) the direction of unit vector u, v and…

Q: Find the domain of the vector-valued function t R(t) = tan-¹t² + —_— 3 + sin t² k. 1-1²

A: Given the vector valued function R(t)=tan-1t i^+t1-t2j^+sin t2k^. We have to find the domain of…

Q: 7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t = 1):…

A: Let us solve above problem

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Q: On a metal plate in the shape of a rectangle, the temperature at a point (x,y) is given by; 100 3x²…

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Q: Consider the following function. T: R? - R, T(x, y) = (2x?, 3xy, y²) Find the following images for…

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Q: The motion of a point on the circumference of a rolling wheel of radius 5 feet is described by the…

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Q: For the vector-valued function r(t) = (cos 2t, sin -(cos 2t, sin-4) 3 (4) what is the magnitude of…

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Q: Show that the vector-valued function shown below describes the function of a particle moving in a…

A: Part - 1 : Given vector-valued function is                                      rt = 5i +5j +3k +…

Q: 2 Consider the vector-valued function R(t) with Ả'(t) = (sec²(t – 1), √t' (a) Find R(t) given Ả(1) =…

A: a) Given: R'→t=sec2t-1, 2t, -2 and R→1=1, 0, -1 To find: R→t