The vector function r(t) (5 – 2 sin t) i+ (3+2 cos t) j+ 2k traces out a circle in 3-space as t varies. In which plane does this circle lie?

Q: Given the triangle ABC, let u= CA/2+ CB/3. (a) Explain why there is and is unique the point X on…

A: Explanation for part a) is correct and sufficient.  For unique point, two vectors intersect at a…

Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

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Q: The vector parametric equation for the line through the points (-3, 5, −4) and (5, −5, 0) is L(t) =

A: The given points are -3, 5, -4 and 5, -5, 0. We have to find a parametric equation.

Q: 5. Find the parametric equations of the line that passes through the point (0, 1, 4)and is…

A: Given two vectors, u=2, -5, 1v=-3, 1, 4 Also, given the point, P=0,1,4 The cross product of u and v…

Q: Consider the line r in the space that passes through points A = (1, 3, −1) and B = (3, −1, 1).…

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Q: Determine the parametric equation for a line that is tangent (intersection) of the two fields below:…

A: We have to find out parametric equation for a line that is tangent (intersection)of the two fields…

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: f. Sketch the curve in the complex plane given by i. Iz - 3| = |z + 3i| ii. z? +z? = 2.

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Q: Give a vector parametric equation for the line through the point (4, 2) that is perpendicular to the…

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Q: Find a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: (c) Use vector methods to find the point P on the circle (x - 5)² + (y-4)² = 4 which is closest to…

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Q: If a line is parallel to the vector 4i + 1j + 4k and passes through the point P = (3, 7,9), then the…

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Q: 3. Find the 1-parametric equation of the line in the plane passing through the vector P=[]-[9] Hint:…

A: p = [-3,2]q = [0,-3]now find parametric equation lines

Q: Find a parametric form for the line through the point (0, –7, -9) and parallel to the vector 6i – 7j…

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Q: A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level…

A: Since you have posted multiple questions. I am answering the first three sub-parts. Please post the…

Q: Find vectors u and v such that the parametric equation of the line y= mx + b can be expressed as…

A: Given that  equation of the line is  y= mx + b…

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

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Q: If a circle passes through the point (0, 0), (a, 0) and (0, b), then find its center. Prove that for…

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Q: Let ä(t) = (5, 4, 2)t + (-6, -4,1) and (u) = (-2, 1, 2)u+ (2, -8,-6). Find the acute angle between…

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