If the line x=1+(a+2)t, y=1-bt, z=-1+(c-1)t and the plane -x+2y-3z=0 are orthogonal to each other. Find a, b and c.

Q: Find an equation of the plane through (-7, 2, 1) that is 2 = 3t, y +3 = 6t, z = perpendicular to the…

A: We know that equation of plane passing through the point (x1,y1,z1) and normal n=ai+bj+ck is…

Q: bugi nе pom the equa that passes 2,1), 2(0, 2, 3) the d P3(−2, −1, −5). Then, find the distance from…

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Q: Find the linear equation of the plane through the point (2,3,6) and parallel to the plane…

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Q: Find the equation of the plane that passes through the point (10, -8, 5) and contains the line y-2…

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Q: Find the equation of the plane that passes through the points A(2, —1, 2), B(1,1, 8) and C(2, 0,…

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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: Determine if the line given by r(t)=(-2t, 2+7t, -1-4t) intersects the plane given by 4x+9y-2z =-8…

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Q: Find the intersection of the line and plane: 3z (2x + y) = -5, P = ( r(t) = (3,-1,0) + t (-3, -2,…

A: Given line : r(t)= (3,-1,0)+t(-3,-2,-1) Given plane : 3z-(2x+y)=-5                       2x+y-3z-5=0…

Q: Determine whether the two planes x-y + 2z = 1 -x-y +z = 3 are parallel or intersecting. Find their…

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Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

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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.