Write an equation for the plane that contains the x-axis and the point (0, 5, 10). O z = 5x + 10y O x = 2y O z = 5y O 2 = x² + y² + z? O z= 2y

Q: Determine if the line intersects the plane. If so, state the solution. [x, y, z ] = [− 1, − 9, 16]+t…

A: The given line is [ x, y , z] = [ -1, -9, 16]  +  t   [ 3, 3, -5]  and the given plane is x+4y+3z=11…

Q: Find the x-, y-, and z-intercepts of the plane. (If an answer does not exist, enter Di 4x - 5y + 2z…

A: for x intercept, y=z=0 for y intercept, x=z=0 for z intercept, x=y=0

Q: Write the equation for the plane. The plane through the point P(-4, -4, 3) and parallel to the…

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Q: Find an equation of the plane.  The plane through the point (2, 0, 5) and perpendicular to the line…

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Q: b). Find the equation of the plane that passes by P(1, -2,3), Q(1,0,1), and the Origin O(0, 0, 0)

A: We have to find the equation of plane.

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

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Q: Find an equation of the plane. The plane that passes through (7, 0, −4) and contains the line x = 3…

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Q: Find a plane through P0(2, 1, -1) and perpendicular to the line of intersection of the planes 2x + y…

A: The directional vectors of the planes are given by (2,1,-1) and (1,2,1)The directional vector of the…

Q: Find the equation for the plane through Po(3,1,9) perpendicular to the following line. x = 3 + t, y…

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Q: Find the equation of the plane through the point (2, 4, 3) that is perpendicular to the line r = (2i…

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Q: Q3/ Find the equation of the plane that contains the line 3-x 2+y %3D 3 - z, and the point P (1, 4,…

A: Given line is  3-x4=2+y2=3-zand the point is (1,4,3) find the equation of the plane

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Write the equation for the plane. The plane through the points P(5, -2, -27) , Q(-3, -4, 25) and…

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Q: Find an equation of the plane. The plane that passes through  (6, 0, −2)  and contains the line  x…

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Q: Find the Cartesian equation of the plane containing the points A(1,0,3), B(1,1,-2) and C(-1,2,0).…

A: Solution

Q: Find the Cartesian equation of the plane containing the points A(4,0,4), B(1,5.5) and C(-1,-1.2).…

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Q: Which of the following points is on the xz plane? a) (1, -3, 0) b) (0, 4, 0) c) (0, 3, -2) O d) (2,…

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Q: X-2 4 y+3 -1 z + 2 3 {3х + 2y + z + 2 %3D 0, х -у+ 2z-1 %3D 0}

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Q: 1. Find the equation of the plane that contains the line point (1,3, 2). 무 =D북3부 md the

A: Let's find.

Q: Find an equation for the plane through A(0,0,1),B(2,0,0),C(0,3,0).

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Q: Q3// :- Write an equation for the plane containing points P=(1,1,-2),Q=(0,2,1), and R=(-1,-1,0)

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Q: Write the equation for the plane through the points P(-1, -7, 45), Q(2, 3, -6) and R(1, -4, 33).…

A: Here we have to find the equation of the plane through the points P(-1,-7,45),Q(2,3,-6) and…

Q: Find an equation for the plane through A (0,0,1),B(2,0,0),C(0,3,0).

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Q: Find the equation of the plane with the given description. Contains the lines r1(t) =〈2, 1, 0〉+〈t,…

A: Find the equation of plane containing two lines: r1t=2,1,0+t1, 2, 3 and r2t=2,1,0+t3, 1, 8.…

Q: B) Find an equation for the plane through A(3,3, 3), B(5,5,5) and C(0,5,9).

A: Given the points are A(3,3,3) , B(5, 5, 5) and C(0, 5, 9) Equation of the plane passing through…

Q: Find the equation of the plane through the point (2, 4, 3) that is perpendicular to the line r = (2i…

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Q: Write an equation for the plane that contains the x-axis and the point (0, 8, 24). O 3 = x² + y? +…

A: Please refer the attached image for complete solution.

Q: Find an equation for the plane that passes through the following points. (2, –1, 4), (0, 0, 6), and…

A: Explanation of the solution is given below...

Q: Find an equation of the plane. The plane through the origin and the points (1, -2, 7) and (8, 3, 1)…

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Q: O Find the equation of the plane that palses through the points A - (2,4,-3), B = (3,-1,5) and 2 :…

A: In the given question we have to find the equation of the plane passes through the points A ,B and…

Q: Write the equation for the plane. The plane through the point P(2, - 2, - 3) and parallel to the…

A: By the using properties we find the required equation of plane.

Q: 2. Find the coordinates of the y-intercept of the plane (x, y, z)=(4,6,5) +s(2,3,1) + t(3,6,12)

A: To find out the coordinate of y-intercept.

Q: Write the equation for the plane. The plane through the point P(-4, -1, -6) and perpendicular to…

A: GIVEN: Point P (-4, -1, -6)  Line x = 10 + 4t, y = 7 + 3t, z = 1 + 5t

Q: Write the equation for the plane through the points P(-1, 1,-12), Q(2, 8, -49) and R(1, -6, 45). 4x…

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Q: Find an equation of the plane that passes through P(4, 2, – 3) and is perpendicular to the line x+1…

A: Given that the plane is passes through the point (4,2,-3) and perpendicular to line x+1-3=y-12=z2

Q: Find the equation of the plane that contains the point A(1, 2,-4) and is perpendicular to the…

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Q: Find an equation of the plane that passes through the points A(2, 1, 1), B(-1, -1, 10), and C(1, 3,…

A: Here we will find out the required equation of plane

Q: Write the equation for the plane through the points P(-1,6, - 61), Q(2, - 8,66), and R(1,- 7,53). O…

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Q: Write the equation for the plane. The plane through the points P(5, 8, -33), Q(-3, -6, 19) and R(-1,…

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Q: Write an equation for the plane that contains the x-axis and the point (0, 5, 15). O 3 = x² + y² +…

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Q: Write the equation for the plane. The plane through the point P(4, 8, 9) and perpendicular to the…

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Q: Find an equation for the plane through A(0, 0, 1), B(2, 0, 0), and C(0, 3, 0).

A: The given point is A(0, 0, 1), B(2, 0, 0), and C(0, 3, 0).

Q: Find the equation of a plane that contains the lines and - 2+5. O A 2x-y-22 = 42 O B. 2x y 2z -10 O…

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Q: Write an equation for the plane that contains the x-axis and the point (0, 6, 12). O x = 2y O z = 6x…

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Q: Find an equation of the plane. The plane that passes through the point (2, 4, 5) and contains the…

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Q: Find an equation of the plane that passes through the points P, Q, and R. P(1, 2, 3), Q(2, 3, 4),…

A: Given, The points are P (1, 2, 3), Q(2, 3, 4), R(3, 6, 9).

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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