Find parametric equations of the line perpendicular to the yz-plane passing through the point (-3, –4, –7). (Use symbolic notation and fractions where needed. Choose the positive unit direction vector.) x = y = z =

Q: a) Find the best straight line fit to the given data points (-3,7), (1,–1),and (3,–7). b) Find the…

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Q: Complete the parametric equations for the line where the planes - 5x – 2y + 2z = 2 and - 13x + 10y +…

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Q: Find the symmetric and parametric equations of the line containing the origin and is perpendicular…

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Q: Complete the parametric equations for the line where the planes – 3x – 9y – 12z - 11x + 2y – 10z 33…

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Q: Complete the parametric equations of the line through the point (-6,0,-8) and perpendicular to the…

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Q: 32. y=-4x+1 a. x=t b. . C. x =-4t /27

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Q: h) Find a parametric representation of the Parabolic equation z = 9(x² + y²)

A: Parametric representation of the Parabolic equation z = 9(x² + y²) will be cartesian coordinates as…

Q: Complete the parametric equations of the line through the points (4,-8,1) and (-7,2,-2) x(t) = 4 –…

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Q: D) Find the parametric and symmetric equations of the line through the points(1, and (-5, 4, 2).

A: Given query is to find the equation of the line.

Q: Find parametric equations for the line that passes through the points P and Q. P(1, –2, 3), Q(5, 1,…

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Q: Complete the parametric equations of the line through the point (-2,-4,-8) and perpendicular to the…

A: Given: Equation of plane x-3y-5z=2 Point (-2,-4,-8)

Q: Find parametric equations of the line through (-1, –1, 6) that is parallel to 2i – 4j+k. x(t) = y(t)…

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Q: The parametric equations for a line L7 are as follows: x=-3-2t y 3+2t z = 1-6t Let L, be the line…

A: Find the point P.

Q: Complete the parametric equations of the line through the point (6,-6,8) and perpendicular to the…

A: Line passing through the point 6, -6, 8 and perpendicular to the plane 7x+2y-3z=-8. Since the line…

Q: Find parametric equations for the line through P = (2, 5) perpendicular to the line y = 4x − 3.

A: Given line, y = 4x − 3. To find the parametric equations for the line through (2,5) and…

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: S¤(t) = – 5t2 ly(t)…

A: Given query is to find the equation in Cartesian form.

Q: Eliminate the parameter in the parametric equations a(t) = –8t – 9 and y(t) = –32t + 9 to write a…

A: Given parametric equations, x(t)=-8t-9 y(t)=-32t+9

Q: Use t = 4x + 1 to write the parametric equations that can represent y = 12x + 5. Ox-y=31-2 Ox-4:…

A: Given that:t=4x+1To find parametric equation for y=12x+5

Q: Find the parametric equations of the line r = ⟨1, 2, 3⟩ + t(4, 0, -6⟩.

A: Given: r→=1,2,3+t4,0,-6 for any given vector equation of line r→=a,b,c+tp,q,r, parametric equation…

Q: Find parametric equations for the given curve. (x - 1)2 + ( y + 2)2 = 9

A: Given: x-12+y+22=32 for any given curve equation x-a2+y-b2=r2, parametric equation of curve is given…

Q: (a) Write the parametric equations of the line through the point (7,3,0) and perpendicular to the…

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Q: Complete the parametric equations of the line through the points (1,-2,2) and (4,-3,6) a(t) = 1+ 3t…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for fæ(t) =…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for Sa(t) =…

A: Cartesian Equation of a Line: The equation of a line in cartesian form is given by y=mx+c, where m…

Q: Express the given parametric equations of a line using bracket notation and also using i, j. k…

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Q: Find parametric equations for the line through P0 = (3, −1, 1) perpendicular to the plane 3x + 5y −…

A: A line L in sace with direction vector d=d1,d2,d3 that asses throughthe point P=(x0,y0,z0) can be…

Q: Eliminate the parameter t to rewrite the parametric equations as a Cartesian equation Į x(1) = (t –…

A: Given equations x(t)=(t-1)2 y(t)=e3t To convert given equations into cartesian equation we need to…

Q: Eliminate the parameter in the parametric equations #(t) = 2t + 5 and y(t) = 8t equations. Provide…

A: In this question we will simply eliminate parameter t and get an equation between x and y. Solution…

Q: Find parametric equations for the lines in The line through (0, -7, 0) perpendicular to the plane x…

A: we know that equation of line in parametric form which passes through pointx1,y1,z1 and…

Q: Perform a rotation of axes to eliminate the xy-term. (Use x2 and y2 for the rotated coordinates.) xy…

A: Given equation xy - 6x -2y = 0

Q: Write the parametric equations x=3t−1, y=3−3t as a function of x in the Cartesian form.y=

A: Given: The parametric equations x=3t-1 and y=3-3t

Q: Find parametric equations for the line described below. The line through the point P(3, 2, 4) and…

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Q: Complete the parametric equations of the line through the point (4,-8,3) and perpendicular to the…

A: See this solution in below

Q: Complete the parametric equations of the line through the points (7,3,-5) and (0,6,1) x(t) = 7 - 7t…

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Q: For the given parametric equations, find the points (x, y) corresponding to the parameter values t =…

A: Given: x = t2 + t       ,     y = 3t+1  values t = -2, -1, 0, 1, 2

Q: Complete the parametric equations of the line through the point (-3,1,-4) and perpendicular to the…

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Q: Find the parametric equations for the line passing through points P(2, -3, 1) and Q(4, 1, -4)

A: Given points are  P2,-3,1,Q4,1,-4

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: %3D Sa(t) = 4t2…

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Q: (a) Find the parametric equations for the line segment that joins P(1, 0, 1) to Q(2, 3, 1).

A: Given, P(1,01), Q(2,3,1)

Q: Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. (x(t) = 5 - 3t…

A: Please see the answer in step 2

Q: Find the parametric equation for the line where the planes - 3y = 3 and -r - y+ 5z = - 9 intersect.…

A: The intersection of two plane is a line or the overlapping plane. Direction of the line is…

Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for Sa(t) =…

A: We have to eliminate the parameter t to find a simplified cartesian equation of the form y = mx+b.…

Q: B Find the parametric equation of the plane passes through the point (-3,0,7) and perpendicular to…

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Q: Find the parametric equations of the line L which is parallel to the line L1 : 2x = 5y = 7z and…

A: The parametric equation of a line L that passes through a point a and parallel to a line r is given…

Q: Write the parametric equations x = 5t – t, y= 2 – 5t in the given Cartesian form. x =

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Q: Complete the parametric equations of the line through the point (8,6,-2) and perpendicular to the…

A: equation of line passing passing through the point 8,6,-2 and perpendicular to the plane , x-7y-z=-3

Q: Find parametric equations for the given curve. 9x2 + 4y2 = 36

A: Given -            Parametric equation -              We define x and y both in terms of a third…

Q: Find the parametric equation of the line passing through P (1, 2, 3) and perpendicular to the lines…

A: Given:  r1= (2+t)i + (1+2t)kr2=(-t)i + (1-6t)j - (2t)k

Q: Eliminate the parameter t to find a Cartesian equation in the form x = = f(y) for: S¤(t) = 2t? ly(t)…

A: The solution are next step..

Q: Find the parametric equation of the line through (1, 0, -2) and parallel to the line % (x – 4) = ½…

A: according to our guideline we are supposed to answer only the first question if you want any…