A spring gun located at the origin O = (0,0,0) fires a ball at time t = 0 at an angle of 30°. The ball hits the floor at P = (V2, 1,0). A light source located at L (0,2,0) casts a shadow of the ball onto a wall behind it. The wall is given by the cquation 2y - V2r = -4. (a) Find a vector parametrization for the position of the ball. (b) Find a vector parametrization for the position of the shadow of the ball.

Q: Q1 Given A= 3i-7j+5k, B = -i+7j-k, C = 4i-j+k. Find the unit vector of: (а) А-В+С (b) АхСхВ

A: The vector addition can be performed by the addition of the respective elements. The elements with…

Q: Given the points M[0.1, -0.2, -0. 1), N(-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: (a) the vector…

A: This question can be solved using the concept of finding the vector joining two points and dot…

Q: Find a vector equation with parameter t for the line through the point (7,0, –7) and parallel to the…

A: We have to find a vector equation with parameter t.

Q: (c) the horizontal. The stone moves in a vertical plane under gravity where the acceleration due to…

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Q: A particle moves in two dimensional space where i and į are unit vectors in the x and y directions…

A: given  r→=6t-4t2i^+2t j^ a) write down the particle's velocity vector in component form. ii) find…

Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

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Q: Determine the direction in which f = x²y√z has maximum rate of increase from P = (8,3,8). Express…

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Q: A particle moves at constant speed 1445 units along the curve of intersection of the two the two…

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Q: 1. Given the points P=(3,-1,-2) and Q=(2, 4, 0) answer or do the following: a) Find i = PQ :_ b)…

A: We can write the points P and Q as P→=3i-j-2k and Q→=2i+4j-0k. We have to find the vector v where…

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: Write parametric equations of the line L through the point P: (2, 0, -3) and parallel to the vector…

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Q: The position of a moving particle in space is vgiven by r(t) = (- 76- 21) i + (108t° - 2890) j +…

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Q: The point A has position vector i+5k and the line l1 has vector equation r=7i+4j–2k+ a(5i+3j+k). (a)…

A: The position vector of point A is given by i+5k. The line l1 has vector equation…

Q: For parts (a)-(e), please use the following vectors: C = (-1,-1,0) -120°, and 0₂ = 90° A = (2,4,0) B…

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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.