2. Find the vector, parametric and cartesian equation of a plane that contains the points А(-1,0, 1), В (0, 1, 2), С (1, —1,0)

Q: 1 Find equation of plane which is containing Points A(2,1,1) and B(7,5,2) and normal to 2 x - 3y -…

A: We have to find the required plane

Q: Find the equation of a plane that is perpendicular to the vector – i+ 2j+ 2k and passing through the…

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Q: 6. Find the vector, parametric and scalar equations of the plane that contains the points A(-1,2,5)…

A: The points are A(-1, 2, 5) B(3, 2, 4) and C(-2, -3, 6) AB→=324--125=20-1AC→=-2-36--125=-3-51 The…

Q: Is the line x = 6- 3t, y = 8 + 8t, z= -t parallel to the plane 3x + y -z=2? Give reasons for your…

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Q: Find the vector equation for the line of intersection of the planes 5x +y-3z= -3 and 5x + z = -1 r =…

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Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: 4 - x y + 1 %3D 2 1 3 L2 :[x, y, z] = [-2,4,3]+ t[-6, 5, 7], t E F

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Q: 1. Find an equation of the plane that contains the line r = -2+ 3t, y = 4+2t, z = 3 - t and is…

A: We have to find

Q: 2. The plane containing the point P(Xg» Yor Zo) and having the normal vector n = (a, b, c) is…

A: Equation of a plane passing through the point Px0, y0, z0 and perpendicular to the vector n=a, b, c…

Q: Determine the parametric equation of the plane that contains the line y-3 *+2-³-² and the point…

A: Virtual find the standard form of the plane then by satisfying the parametric values we will…

Q: Verify that it’s possible for a line with direction vector   d=(2,1,-2) to lie flat on a plane with…

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Q: 4. Find an equation (in point-normal form) of the plane containing the points K, M, and N. 5. Let R…

A: This is a problem of Vector Algebra.

Q: Find the vector equation of the line of intersection of the planes x+y+z=1 and x+2y+2z=1.

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Q: Find the equation of a plane that is perpendicular to the vector i+ 2j+5 k and passing through the…

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Q: The equation of a plane n ·〈x, y,z〉= d is said to be in normal form if n is a unit vector. Show that…

A: Given :           The equation of a plane n . <x, y, z> = d is said to be in normal form if n…

Q: snip1

A: we have to find the normal and general forms of the equation of the plane that contains the point…

Q: Find an equation of the plane containing the line = 3t, y=2-4t, z = 1+ t and parallel to z-axis.…

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Q: Answer the question in the picture.

A: Concept:

Q: Find an scalar equation of the plane containing the line x = 2 – 4t, y = 4 – 5t and z = 5+t and the…

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Q: 10.Determine the vector equation of the plane that contains the origin and the intersection of:…

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Q: Find the general equation of the plane containing the point (2,-1,4) and normal to the line 2 I+3…

A: The equation of the line passing through the points x1,y1,z1 with direction ratios a, b and c is…

Q: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

A: Let M be a plane that contains the point with coordinates -2, -2, -1 and is orthogonal to the vector…

Q: Find the scalar equation of the plane that contains the line x+1 -3=. and is parallel to x+2=+4_:+2…

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Q: Find the vector equation for the line of intersection of the planes 2x – 2y – 5z = 5 and 2a + 2z = 1

A: Given  equation of planes 2x-2y-5z=5 2x+2z=1

Q: Find an equation of the plane satisfying the given conditions.

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Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

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Q: Find a scalar (Cartesian) equation of the plane that contains the origin and the point  (2, -3, 2)…

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Q: 4) a) Find the vector parametric equation of the line in R³ that is perpendicular to the plane 2x -…

A: Given plane is, 2x-3y+7z-4=0

Q: Find the vector equation for the line of intersection of the planes 5x + 4y + 5z = 1 and 5z + z = -4…

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Q: 2. Find an equation of the plane determined by the points P(1,1,0), Q(1,0,1) and R(0, 1, 1).

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Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y²…

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Q: 2. Write the plane equation when it passes through a point Mo(11,2) and is: a) perpendicular to the…

A: We have to find the equation of the plane.

Q: Find the general equation of the plane containing the point (2, –1,4) and normal to the line 2 = =…

A: As the line is normal to the plane, the DRs of the line and normal of plane is same.

Q: Find an equation of the plane through the origin that is parallel to the plane 5x – 4y + 6z + 10 =…

A: Here we have to find the equation of a plane.

Q: 4. What is the equation of the plane through (1 ,2,3) parallel to the plane x- 2y + 3z = 9? (a) x 2y…

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Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

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Q: Find the vector equation of the line of intersection of the planes x+y+z = 1 and x+2y + 2z = 1.

A: The equation of the line vector of the intersection of 2 planes can be calculated using the cross…

Q: a)Find the equation of the plane in 3- dimensional space passing through the points P = (1, 2, 1), Q…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the value of d in the equation of the plane ax+by+cz+d=0 passing through the point P(3, 1, -2)…

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Q: Write the parametric and scalar equations of the plane given its vector equation [x, y, z] = [4, 3,…

A: Parametric equation is simple: x = 4 + 2s + 6t y = 3 + s + 6t z = -5 + 4s - 3t

Q: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

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Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 6z + 18 =…

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Q: Find the vector equation for the line of intersection of the planes x – 5y + 2z = 1 and æ + z = 1 |…

A: To find the vector equation of the line of intersection of given planes.

Q: (3) Write the equation of the plane which is perpendicular to the vector ñ² = (2₁-1₁-2) and touches…

A: To find- Write the equation of the plane which is perpendicular to the vector n→ = 2, -1, -2 and…

Q: 3. Find the equation of the plane parallel to the plane with equation 18x + 6y – 5z = 0 and passing…

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Q: 10. Determine the scalar equation of a plane that is perpendicular to the line: |1,2, 3| + t|-2,4,…

A: A normal of a plane perpendicular to the line will be parallel to the line. So the plane is:…

Q: 2. Find the equation of plane which passes through the point (1,2, –3) and the vector i – 2j + 3k is…

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