The curves ri(t) = (4t-t²,3t, ²-4) and r₂(t) = (4-t,t³ +8,5t) intersect at the point (3,9,5). If u and v are the tangent vectors of the two curves at this point, then find a vector perpendicular to u and v.

Q: = (4, 1, a), Q = (–2, 0, b) and v = i – 3j + 4k be two points and a vector in R³ respectively. (a)…

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Q: Let C = (-2, -1) be the center of dilation. Let X = (1, 1), Y = (3, 0) and Z = (2,5). Our dilation…

A: Center of dilation=-2, -1X=1, 1, Y=3, 0, Z=2, 5Dilation factor, k=3

Q: The vector describing a particular particle is given by F (t) = Rcos (wt) î + R sin (wt) ĵ, where R…

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Q: A vector equation for the line through the points A (3, -4, -3) and B (3,4,2) is (x, y, z) = . (You…

A: Concept to be used:If a line passes through two points A,Bwith position vectors aand brespectively,…

Q: (c) the horizontal. The stone moves in a vertical plane under gravity where the acceleration due to…

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Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

Q: Find the velocity vector v(t), given the acceleration vector a(t) = (3e¹, (Use symbolic notation and…

A: Formula for the acceleration is We have and the initial velocity

Q: Find all points on the curve r(t) = ti + t²j+t³k where its tangent line is parallel to the vector…

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Q: The scalar component of H parallel to the line y=1, z=2 where H = -2a, + 3as- 4a, at p (1,90, 2) -3…

A: Given: H=-2aρ+3aϕ-4az p=1,90,2

Q: A missile is fired from ground level with an initial velocity of (0) - (1000, 1400, 368) measured in…

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Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: (a) Find the direction for which the directional derivative of the function f(x, y) = 9xy + 2y is a…

A: Formula for directional derivative Du→fP=∇f(P).u^=∇f(P)u^cosθ Du→fP to be maximum angle θmust be 0.…

Q: A particle P moving a constant velocity i+j+ k passes through a point with position vector 3i – 7j -…

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Q: The point A has position vector i+5k and the line l1 has vector equation r=7i+4j–2k+ a(5i+3j+k). (a)…

A: The position vector of point A is given by i+5k. The line l1 has vector equation…

Q: Let Q(t)= t i + t-1 j. a) draw the vectors Q(1), Q(2), Q(3), Q(4), and Q(5). b) Add a sketch of the…

A: Part (a)Please see the table below and the plot on the white boardtQ(t)= ti + t-1j.xy1Q(1) = i +…