Find a piecewise smooth parametrization of the path C (the edges of the triangle in space with vertices: (0,0,0), (0, 1, 0), and (0, 1, 1)). Then evaluate the line integral (2x² + y² - z) ds.

Q: Parameterize the intersection of z = - Vx² + 7y² _and x² + y? + z? = 200

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Q: Find three different parametrizations of the graph of y = x3.

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Q: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

A: We know that equation of line passing through the points (x1,y1,z1) and (x2,y2,z2) is

Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

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Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

Q: [1 |A = [a1, a2, a3, a4] 2 11 5 0 3 -1 4 0

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Q: Parametrize the directed line parabolic segment y = x2 that joins 2 + 4i to −1 + i.

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Q: Line A goes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A and passes…

A: Given: Line A passes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A. Line…

Q: Find an equation of the plane through the three points given: Р - (0,5, 0),Q — (2, 1, —4), R —…

A: The given points are P=(0,5,0), Q=(2,1,-4), R=(-1,1,-3) We have to find an equation of the plane…