Points A(1, 0,0), B(0, 2,0), and C(0, 0, -3) lie in a plane.  Find a vector orthogonal (perpendicular) to AB and BC .  Show that the vector you found is also orthogonal to CA.  Write an equation of the plane containing these three points

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: 2. Given a line that passes through the point (-2,1,3) and is parallel to the line joining A(1,5,3)…

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Q: Write down the vector equation of the line passing through the points with position vectors p=…

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Q: 1 Determine a vector equation of the line passing through the points A(-2, 0, 0), and B(0, 1, –3). *…

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Q: Find the vector and parametric equations of the line through the points A = (2,4,7) and B =…

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Q: Let P be the point (-1,0, 2). Consider the plane that goes through the points A = B= (1, -3, 3), and…

A: First of all let us find out the equation of a plane passing through the points…

Q: Determine whether the lines L₁ and L2 given by the vector equations are parallel, perpendicular, or…

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Q: Please no written by hand solutions 13 x^(3)+4x-(x-6)^(2)-(7x^(2)+4) Which of the following…

A: Given polynomialf(x)= x³+4x-(x-6)² -(7x²+4)know that (a-b)²=a²+b²-2abnow by using this we…

Q: Determine whether the lines L1 and L2 given by the vector equations are parallel, perpendicular, or…

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Q: he vector v = ai + bj is parallel to the line bx – ay = c. Use this fact to find ector starting at…

A: Introduction: The formula for the equation of the line passing through a point P(a,b) is given by,…

Q: perpendicular to (x, y, z) = (1, -2,0) + r(1, -1, 1) through P(1, 3,5) [parametric equations]

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Q: A point A(-5,-3) is translated by the vector v = , and then reflected about the line y=0. the…

A: Given that: A(-5, -3) is translated by v=<8, 0>

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: Consider the line passing through the points (2, -3,4) and (5,10, -12). Describe the line by a.…

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Q: Find the vector equation of the line that goes through the point (18, 11, 20) and is perpendicular…

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Q: 3. Give the parametric and symmetric equations of the line that passes through the point (4,-3,5)…

A: Hint: A vector v→ is perpendicular to both a→=a1i^+a2j^+a3k^ and b→=b1i^+b2j^+b3k^ if v→=a→×b→…

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.