The surface of a hill can be given as h(x, y) = e-(z²+y²), If a ball is placed at the (2, y) coordinates of (1, 1), in which direction will the ball roll? Express your answer as a vector (it need not be a unit vector.)

Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

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Q: Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

A: Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation for…

Q: By finding the extreme values of f, find the shortest distance between Lị and L2. Be sure to fully…

A: Given that L1: v=2,4,4+t4,1,5L2: v=1,−3,2+t−2,3,1 To find the shortest distance between L1 and L2.

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

A: The equation of the line vector of the intersection of 2 planes can be calculated using the cross…

Q: Find the vector equation of the line (d) through (6, −3) and parallel to the line through (5, −1)…

A: First, we find the slope of the line  through (5, −1) and (2, 11) Direction vector is=(2, 11)-(5,…

Q: Given the same three points P (1, 4, 6), Q (-2, 5, -1)  and R (1,  -1, 1).  Find a vector equation…

A: We can find vector equation of the line segment from Q to R .

Q: Find the scalar equation of the line through (3,-2) and perpendicular to the line r = (4,-3) +…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.