Find the plane z = a + bx + cy that best fits the data points (0, –4, 0), (5,0, 0), (4, –1, 1), (1, –2, 1), and (-1, –5, –3).

Q: Find a plane containing the point (6,-7,7) and the line x(t) y(t) z(t) = = = - 2 - 6t - 1 + 5t 5-t

A: Here we have to find the equation of plane

Q: Find the equation of the plane through (1,2,3) and parallel to the plane: x+y=-2-z

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Q: Q1// A :- Find an equation of the plane that passes through point (1,4,3) and contains the line…

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Q: Obtain the equation of the plane that passes through the points: A (2, 1, -1), B (5, -2, 0), C (0,…

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Q: Find an equation for the plane in R³ spanned by the points (1,5,

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Q: Find the Cartesian equation of the plane containing the point P(1,3,-2) and the I T = (0, -1, 4) +…

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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 plane z = a + bx + cy that best fits the data points (0, -4, 0), (5, 0, 0), (4, –1, 1), (1,…

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Q: Find equation of the plane that contains the lines L1:x = 3 + 5t, y = 6+ 2t, z = 6 + 3t and L2: x =…

A: Equation of plane which passes through L1 is ax-3+by-6+cz-6=0 where 5a+2b+3c=0.

Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

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 passing through the points O = (0,0,0), A = (-2,–2,1) and B= (-1,0,…

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Q: Find the equation of the plane parallel to the intersecting lines (1,2 +t, -3 – 3t) and (1 – t, 2 –…

A: Let, the direction vector of 1,2+t,-3-3t is v1=0,1,-3 and the direction vector of 1-t,2-3t,-3-2t is…

Q: find an equation for the plane through pointsP, Q, and R. P(1, 0, 0), Q(0, 1, 0), R(0, 0, 1)

A: Given points are Here the objective is to find the equation of the plane passing through points P,…

Q: Find an equation of the plane passing through the three points given.P = (5, 1, 1), Q = (1, 1, 2), R…

A: GivenP=(5,1,1) , Q=(1,1,2) and R=(2,1,1)To find equation of plane passing through the three points.

Q: Find the plane z = a + bx + cy that best fits the data points (0, -4, 0), (5, 0, 0), (4, -1, 1), (1,…

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Q: Find an equation of the plane. The plane that passes through the point (1, 3, 5) and contains the…

A: Given linex=5t , y=1+t , z=3-tDirection vector of this linev⇀=5,1,-1coefficients of t

Q: Find the equation of the plane containing the point P(1, 1, –1) and the line -4+t 1- t 1+t

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Q: Find the equation of the plane passing through the three points A = (-1,0, 2), B = (2, –1, 2), C =…

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Q: Find the equation of the plane passing through the three points A = (-1,0, 2), B = (2, –1, 2), C =…

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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 = 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 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 equation of the plane: The plane that passes through the point (3, 4, 5) and contains the…

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Q: Find a plane containing the point (-3,3,-3) and the line F(t) = +t

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

A: given plane pass through the point(3,-1,4)

Q: Find the point of intersection of the line x-9 = - 5t, y +1= -t, and the plane 2x – 3y + 4z + 7 =0-…

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Q: Find the equation of a plane that passes through the point (0,0,0) and contains the line x = 2 -t y…

A: Here we have to find the equation of a plane that passes through the point (0,0,0) and contains the…

Q: Determine the equation of the plane that contains the points P(1,−2,0), Q(3,1,4) and R(0,1, -2)

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Q: Find the equation of the plane passing through the three points A = (-1,0, 2), B = (2, –1,2), C =…

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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: Determine the equation of the plane through the points (1, 0, 3) and the line l : ¯r = (3, 4, 1) +…

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Q: Find an equation of the plane that passes through the points M(1,2,3), N(-3,-2,5), and O(2,-3,4).

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Q: Find the general form of the equation of the plane containing the point Q(0, –2, 10) and the lin l1…

A: Let's find.

Q: Find the equation of the plane that contains the following two lines: I = -1+t, L1 : y = -t, I = -1,…

A: To find the equation of plane containing both the lines

Q: 1. Find the equation of the plane that passes through the points P(2,0,1), Q(1,0,-1) and R(3,0,1).

A: We have, Vectors in the plane are, Therefore, equation of plane passes through 3 points will be,…

Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

Q: Find the equation of the plane that contains the line 2 5-x 2+y – 5 – z, and the 3 point P( 0,5,2).…

A: We have to find the equation of the plane that contains the line and the point.

Q: Find the equation of the plane through the points P (1,-1, 1) Q = (3,–1,3); R= (2,1,1).

A: We will find out the required equation of plane.

Q: Find an equation for the plane containing the three points P = (1, 2, 3), Q = (3, 1, 2), and R = (2,…

A: To find an equation for the plane containing the three points P = (1, 2, 3), Q = (3, 1, 2), and R =…

Q: Find the equation of the plane through the point P = (3, 2, 5) and parallel to the plane a + 3y+ 3z…

A: Given: Line is parallel to x+3y+3z = 5 Equation of the plane parallel to the plane x+3y+3z = 5 is…

Q: Find the equation of the plane for all points equidistant to (1, -1, 1) and (0, -5, -2).

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Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

Q: a) Find an equation of the plane passing through the points P=(1,–2,0),Q=(3,1,4) and R = (0, –1,2).

A: Given points are P1,−2,0, Q3,1,4, R0,−1,2. We have to find the equation of the plane passing through…

Q: Find the equation of the plane whose has the line x=2-3t, y=3 + t, z = 5t and passes through the…

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Q: An equation of a plane P passes through the point (0,0,3) and perpendicular to the line L:x =1– 2t,…

A: Given,          An equation of a plane P passes through the point 0,0,3 and perpendicular…

Q: Determine the general form of the equation of the plane passing through P(2,1,-1), Q(0,-2,0) and…

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Q: Find the equation of the plane passing through the three points A = (-1,0,2), B= (2, –1,2), C = (3,…

A: Given problem:- Find the equation of the plane passing through the three points A = (- 1, 0, 2) B =…

Q: Find the equation of the plane that contains the points P(-1,2, 1), Q(0, -3, 2), and R(0, 1,-4)

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Q: Find an equation for the plane containing the two (parallel) lines v, = (0, 1, –4) + t(1, 3, –5) and…

A: Solution: The objective is to find an equation for the plane containing the two parallel lines

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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