Use the vector cross product to nd the equation of the plane in R3 containing the three points (4,1, 2), (1, −1,1), (5, 2, 3).

Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1, and a z-intercept of 5.…

A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: The line (x-22-3, y = 2z) intersects the plane (x+3y-2+4= 0) at the point P, Find: a) the…

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Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

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

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Q: 2. Find the equation of the planes: a) (in general form) that goes through the three points A(4, 0,…

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Q: III. Consider the line ₁ given by the symmetric equations +1=-y-1 B 2 and the line ₂ given by the…

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Q: Find the vector equation of the plane that contains the parallel lines [x, y, z]= [0,1,3] + [-6,…

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

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Q: - 3)² = 81 then, find its ce or a=<3, -1

A: 1. Given: The points are 2,3,-6 and -1, 4, 5 To find the distance between the given points. The…

Q: Q8. Find the equation of the plane passes through the point (1,2,3), parallel to the vector…

A: We have to find the equation of a plane passing through a given point and parallel to two vector.…

Q: Find the vector equation of the plane taking into account that 4x - y - z = 3

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