Find the parametric equation for the line in R' that passes through the point (1, –2, 3) and that is parallel to the vector (-1,0, 5). Sketch this line.

Q: r(t) = (sin 7t, t, cos t)

A: The vector equation is r(t)=sinπt, t, cosπt. Here, x=sinπt, y=t, z=cosπt Then x=sinπy, and z=cosπy…

Q: Find the standard vector parametric equation of the plane curve given by 24x + 6y + 96 x- 48 y +96 =…

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Q: Find a set of parametric equations for the line passing through the point (2, 0, 9) that is…

A: a set of parametric equations for the line passing through the point (2, 0, 9)  that is parallel to…

Q: Find a set of parametric equation of the line through the point (1, 0, 1) parallel to the line x = 3…

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Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: Sketch the curve defined by the parametric equations x = t2, y = t + 1, -∞ < t < ∞.

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Q: Find parametric equations of the line through (-1,0,3) that is parallel to 5i – 6j+k. x(t) y(t) =…

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Q: Find parametric equations for the line through (- 1,6, - 1) perpendicular to the plane 7x+ 5y + 5z =…

A: to find the parametric equations for line passing through (-1, 6, -1) and perpendicular to the…

Q: Find parametric equations for the lines in The line through the point P(3, -4, -1) parallel to the…

A: Given P3,-4,-1r=ro+tvro=3,-4,-1,ro=3i∧-4j∧-k∧v=i∧+j∧+k∧

Q: Find the vector parametric equations of the two straight lines tangent to the given space curve

A: Given,              rt=2t2+3i+15t-7j+4t2+5kand  passing through the point P-3, -22, -7.

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

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Q: Find a parametric equation of the line tangent to 7 (t) at the point (– 12, 144, – 4.159)

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Q: Find the parametric equations for the lines. Where, the line through the point P (3, -4, -1)…

A: Topic = Vector

Q: Find a parametric equation for the line through the point(1,9,3) and perpendicular to the plwne…

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Q: find the parametric equations of the line through (-3,0,2) that is parallel to 3i-4j+k. x(t)= y(t)=…

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Q: Find the parametric equation of the line that passes through P(-2, 0, 3) and is parallel to the line…

A: Given that: Equation of line is:     x=-1+3t, y=2-2t, z=3+t  and the point is : P(-2, 0, 3)

Q: Find parametric equations of the line through (-3,0,9) that is parallel to 2i-6j+k. x(t)= 11 y(t) =…

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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: 5. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

A: To find the parametric equation of the given tangent to the curve. The vector equation of the curve…

Q: Find parametric equations of the line through (-3,0, 4) that is parallel to 5i– 8j+k. x(t) y(t) =…

A: Parametric equations of a line passing through the point P(a,b,c) and parallel to the vector v→=…

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 the parametric equations of the line contains point P (2, -1, 2) and tangent to the vector v =…

A: Given problem:- Find the parametric equations of the line contains point P (2,-1, 2) and tangent to…

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

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Q: Find the distance from the point (3, 2, 5)to the line with parametric equations x=t,y =l +t ,z = 2 +…

A: The equation of the line in matrix form:                                                xyz = 012 +…

Q: Complete the parametric equations for the line where the planes - 7x + y + 3z = 3 and 4x7y + z = 23…

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Q: The planes 5x+y+z=−6 and 3y+5z=22 are not parallel, so they must intersect along a line that is…

A: Given planes are 5x+y+z=-6 and 3y+5z=22 find the vector parametric equation

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 3x + 4y +…

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Q: Find the parametric equation for the line where the planes 4x – by + 8z = - 36 and – by + z = – 15…

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Q: Complete the parametric equations for the line where the planes - 7x + y + 3x = 3 and 4x7y + z = 23…

A: Given two planes -7x+y+3z=3 and 4x-7y+z=23

Q: Find an equation of the line through (0,0,0) that is parallel to the e parametric equations x(t) = 2…

A: To find out equation of any line we need one point on the line and a vector which is parallel to the…

Q: Consider the line perpendicular to the surface z=x^2+y^2 at the point where x=3 and y=2. Find a…

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Q: Find the parametric equation of the line that passes through the point (4, -5, 0) and is…

A: We have to find the parametric  equation of the line.

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: Find the parametric equation of the intersection of the planes x + y = 1 and x + z = 2.

A: Equation of plane 1 - x+y = 1        Normal vector of plane 1 = n1 = 1,1,0…

Q: Find the parametric equations for the line through the point (1, 7, 2) that is parallel to the plane…

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Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 4x+2y…

A: Let F(x,y,z) define a surface that is differentiable at a point (x0,y0,z0), then the normal line to…

Q: Find the parametric equation for the line where the planes 7x – 6y + z = 10 and 2x + y – 3z = 4…

A: We have, r(t) = (0, -2, -2) + t(17, 23, 19) The detailed solution is as follows below:

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 4x + y +…

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Q: Find the parametric equations for the line through the point P = (-1, 4, -4) that is perpendicular…

A: Normal vector perpendicular to the plane 2x−4y−2z=1 is: (2, -4, -2) The line passes through P = (-1,…

Q: What is the parametric equation for the line through the point (1,2, 3) paralkel to the y- axis? (a)…

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Q: Complete the parametric equations for the line where the planes -4x + 2y – 14z = – 32 and -x – y –…

A: Use parametric equation of tangent line

Q: Write an equation of the tangent plane to the parametric surface: r(u, v) = (u + v)i + 3u^2j + (u −…

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Q: Find the parametric equations for the line through the point P=(-5,4,-1) that is perpendicular to…

A: The direction vector for this line is v=2,-1,-5 and it must pass through the point -5,4,-1. Thus we…

Q: Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line…

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Q: R(u, v) = (uv, u sin v, v cos u)

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Q: Find a vector parallel to the line defined by the parametric equations x(t) - 3 – 9t y(t) 2 + 7t…

A: Need to find parallel vector and point on the line

Q: Sketch the curve with the vector equation ř(t) = (sin t, t). Indicate with an arrow the direction in…

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Q: Find the parametric equations of the line that is perpendicular to the plane 2x +y +3z = 4 and goes…

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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…

Q: G. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.