Find the point at which the line (-3, 4, 2) +t(-4, 3, 1) intersects the plane -4x + y – 5z = 76.

Q: Q2: Find the equation of the plane that pass through the point P(-1,4,2) and containing the line of…

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Q: Find the point at which the line (3, 4, 5) +t(1, -1, –5) intersects the plane -5x + 2y+ z = -86.

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Q: Find the point on the plane x − 2y + 3z = 6 that is closest to the point (4,2,0).

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Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0,1,1).

A: First we find out normal vector to the given plane than find out the point that is closed to the…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0, 1, 1).

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Q: Find an equation of the plane that contains the point P(5,0,2) and the line x = 3t +1, y=-2t + 4, z…

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Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1and 2x+3y+4z=…

A: The equation of the plane through the intersection of the planes, x+y+z=1 and 2x+3y=4z=5, is…

Q: Find the equation of a plane through the point (- 1,1, 3) and orthogonal to the line ( x(t) = – 7 –…

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Q: Find an equation of the plane through the point (2, 0, 1) and perpendicular to the line x = 3t, y =…

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Q: Find the equation of the plane that contains the point P(3,5,-1) and the linex = 4 - ty = -1 + 2t,z…

A: The plane contains the point P(3,5,-1) and the line x=4-t, y=-1+2t, z=-3t

Q: Find an equation of the plane that contains the line l(t) =(-1,1,2)+t(3,2,4)y which is perpendicular…

A: As given by the question There are given that the equation of line: lt=-1, 1, 2+t3, 2, 4 And, The…

Q: Determine the general equation of the plane 2 passing through the point P(-1,4, 5) and parallel to…

A: Follow the procedure given below.

Q: Find the equation of the plane through the point P = (2, 5, 4) and parallel to the plane 5x – 5y +…

A: Equation of plane parallel to 5x -5y +3z = 6  is given by; 5x -5y +3z + λ  = 6 Also it passes…

Q: Find the point P where the line x = 1 +  t,  y  =  2t,  z = - 3t  intersects the plane x + y - z =…

A: Given line: x=1+t,  y=2t,  z=- 3t

Q: 4) Find the equation of the plane that passes through the point (6,0, 2) and contains the line x = 4…

A: The plane that passes through the point (6, 0, 2) and contains the line x = 4 − 2t, y = 3 + 5t, z =…

Q: A) Find the point at which the line x = 2, y = 3+ 2t, z = -2 - 2t meets the plane 6x + 3y – 4z = -12

A: Given line is x = 2, y = 3 + 2t z = -2-2t and the plane 6x + 3y - 4z = -12

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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Q: Find the point P where the line x = 1+t, y= 2t, z= -3t intersects the plane x+ y -z = -3

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Q: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

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Q: Find an equation for the plane that contains the line x = − 1 + 3t, y = 5 + 3t, z = 2 + t and is…

A: We need to determine the equation of the plane that contains the line: x=-1+3t, y=5+3t, z=2+t and is…

Q: Find an equation of the plane containing the point (1,2,-2), and the line: x= 2t, y= 3-t, and z…

A: To find the equation of plane we need to find its normal vector. To find the normal vector, we…

Q: Find an equation of the plane through the point (2,0, 1) and perpendicular to the line x = 3t, y = 2…

A: To find the equation of a plane passing through (2,0,1) and perpendicular to the line x=3t , y=2-t ,…

Q: Find a plane containing the point (-3,-3,5) and the line x(t) y(t) z(t) = = 8 + 4t -4-6t -7-3t

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Q: Find an equation of the plane that contains the point (2, 0, 3) and the line x =-1+t, y =t, z=-4+21…

A: It is given that the required plane contains the point 2,0,3 and the line x=-1+t,y=t,z=-4+2t. The…

Q: Find the point on the plane 4x+7y+8z−19=0 closest to the point (−2​,1​,3​).

A: Given,

Q: Find the linear equation of the plane through the point (1, 7, 6) and parallel to the plane x + 3y +…

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Q: Find all planes in R^3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

A: To find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.…

Q: Find the equation of the plane containing the point P(-2,4,3) and the line y+1 z+2 %3D 4 2 -3

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Q: Find the equation of the plane perpendicular to the line x 2t, y = 6 - t, z = 4+t and containing the…

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Q: Find the equation of a plane through the point(- 3, – 2, 3) and orthogonal to the line x(t) - 5+ 8t…

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Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

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Q: Find the general equation of the plane perpendicular to the line z – 2 y + 4 1- x = 3 and is 3…

A: We have to find the equation of plane.

Q: Find the point at which the line (-2, 2, 1) + t(5, –4, 3) intersects the plane -4x – 4y + z = -5.

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Q: Find the point at which the line (-4, 1,1) + t(2, -5, 4) intersects the plane -5x+ 3y – 3z = -54.

A: the given line is  xyz=-411+t2-54 xyz=-411+2t-5t4t xyz=-4+2t1-5t1+4t

Q: Find the general equation of the plane perpendicular to the line Z – 2 y+ 4 1- x = 3 and is 3…

A: This is a problem of vector algebra and geometry.

Q: Find the point on the plane x - 2y + 3z = 12 that is closest to the point (0, 2, 2). (x, y, z) =

A: Just I have used the Lagrange multipliers method and find the required solution.…

Q: Give the general equation of the plane containing the point (3,-1,4) and x 2-2 perpendicular to the…

A: The given equation of the linex2=y=2-z-3which can be written asx-02=y-01=z-23.The given point is…

Q: Find the equation of the line containing the point (1, 3, −2) that is parallel to both of the planes…

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Q: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

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Q: Find the point at which the line (-3, -4,-2)+t(5, -4,-2) intersects the plane -5x +3y+z= -155.

A: Given: line equation: -3,-4,-2 +t (5,-4,-2) Then equation of line from parametric equation is given…

Q: A) Find the point at which the line x = 2, y = 3+ 2t, z = -2-2t meets the !3! plane 6x + 3y- 4z -12

A: Here we have to find the point at which the line x=2, y=3+2t, z=-2-2t meets the plane 6x+3y-4z=-12…

Q: Determine the general equation of the plane 2 passing through the point P(1,-4,-5) and parallel to…

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Q: Find an equation of the plane that is parallel to the plane x+ 2y – 10z + 12 = 0 and contains the…

A: The equation of the given plane is  x+2y-10z+12=0 We need to find the equation of plane that is…

Q: A) Find the point at which the line x = 2, y = 3+2t, z = -2- 2t meets the plane 6x + 3y - 4z = -12

A: The line is given by:x=2, y=3+2t, z=-2-2tand the plane is given by6x+3y-4z=-12.We need to find the…

Q: Find an equation of the plane that is passing through the point and is perpendicular to the line L.…

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Q: Find the equation of the plane through the point P = (5, 3, 3) and parallel to the plane 3y – 5x –…

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Q: Find the equation of the plane that contains the point P(-6, 5, 7) and is perpendicular to the line…

A: Use direction ratios of line to find direction ratios of plane. Then use the point to find equation.…

Q: Find the equation of the plane that contains the point P(3,5, –1) and the line = 4 – t, y = –1+ 2t,…

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Q: . Find the equation of the line containing the point (1,3, –2) that is parallel to both of the…

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