Consider the curves r(t) = (4t-3, 2t+2, 6t-1) for -∞ < t <∞ and s(t) = (s + 1,4s + 4,-3s + 5), for -∞ < s < x. (a) (b) Do the lines intersection? If so, find the coordinates. If the r and s describe the path of particles, do the particles collide? Assume t > and s20 in seconds.

Q: = - 1+ 3t Find a plane through the point (7,5,-5) and orthogonal to the line y(t) = – 6 – 3t z(t) =…

A: The given line is: x+13=y+6-3=z-4-2

Q: Find a plane containing the point (-5,-8,-7) and the line x (t) y(t) z(t) = = = −7+ 6t -3 - 2t - 2 +…

A: Given;

Q: x(t) Find the point at which the line y(t) z(t) = = = 4 - 8t -4+ 5t intersects the yz plane. 6 + 2t

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Q: Find the coordinates of the intersection points A and B, between the closed curve (x + 1)² + 4(y-1)²…

A: In this question, we can find the intersection points of the given curve. Using the equation of…

Q: Find the shortest distance between the lines i-(i+2j+k) + 2(i-j+â)and 7= 2i - j-k + 4(2i + j+ 2k)

A: The equation of the given lines are r→=i^+2j^+k^+λi^-j^+k^r→=2i^-j^-k^+μ2i^+j^+2k^ It is known that…

Q: L(t) = (−2,0, 3) +t(2,3,−4), _ne 27x+10y + 21z = 1279. is … -∞<t<∞

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Q: Consider the following lines: r(t) = (3t + 2, 2t +2, 4t + 4), R(t) = (s+ 1, 4s – 2,-5s + 9), -o 0…

A: The given lines are                      r(t)=3t+2, 2t+2, 4t+4   , -∞&lt;t&lt;∞ and…

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A: Equation of the plane general form is  a(x-x_1)+b(y-y_1)+c(z-z_1)=0

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A:

Q: Find equations for the lines tangent and normal to the cissoid of Diocles y² (8-x) = 16x³ at (4,16).…

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Q: The line L(t) = (3+t, 12+5t, -12-5t) intersects the plane 5x - 5y = 15 at what point?

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Q: Find a plane containing the point (-3,-3,5) and the line x(t) y(t) z(t) = = 8 + 4t -4-6t -7-3t

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A: The equation of plane is mainly given by the normal vector calculation. The normal vector to the…

Q: (a) Find two points on the line x = -1+3t, y=t + 2, z= 2t – 7. (b) ( Find The point at which the…

A: Equation are given in parametric form: Vary parametric value for different points.

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A: We have to find the equation of the plane that contains the line and the point.

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: v = (2x² – y² +4)i+(5y+3x – 6)j . Consider two closed paths starting (and ending) at a dock located…

A: Let A=(-1,0), B=(2,0), C=(0,2). Now,∫path 1v.dr =∫path 12x2-y2+4dx+5y+3x-6dy…

Q: The cartesian equation of the curve x= f ,y = 1-t is : (a)y = 1– x², x 20 (b)y =1-x ,x 2 0 (c) x = 1…

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Q: Let A(0,-2), B(0,4) (1) Find the set of all points P(x, y) such that m(PA)=2 m(PB) (2) Convert the…

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Q: Q2:Prove that the line (x-1)/2=(y+1)/3=(z-2)/(4 ) is parallel to the plane x-2y+z=6 ?

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