The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1, -1) is:   a. 4x - y + 9z = 0 b. 4x - y + 9z + 7 = 0 c. 4x + y + 9z = 0 d. 4x - y - 9z = 0

Q: Is the line x = 9- 8t, y= 4 + 2t, z= - 5t parallel to the plane 2x + y-z=2? Give reasons for your…

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

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Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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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 a vector parallel to the line of intersection of the planes 2x + 3y – z =11 and 4x + 2y – 3z =…

A: We need to find a vector parallel to the line of intersection of the planes 2x+3y-z=11 and 4x + 2y -…

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: Find an equation of the plane through the point (2,1,-3) with normal vector 2i-3j+k. Determine the…

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Q: Find the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=<  ,  , 0…

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Q: Consider the vectors a = (-1,–2, 3), b = (3,0, –2), v = (2, –5, –4) and the plane P given by 2x + y…

A: The given vector is; a→=-1,-2,3b→=3,0,-2v→=⟨2,-5,-4⟩and Plane P is;2x+y=z+13⇒2x+y-z=13…

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: Find the scalar equation for the plane passing through the point P-(5, 3,-5) and containing the line…

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 3x−3y−4z=5 and…

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Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

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Q: snip1

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

Q: Find a scalar equation of the plane containing the line x = 4+ 5t, y = 5+3t and z = 6+ 4t the point…

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Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

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

A: Use the direct formula for equation of plane passes through a point and with given normal vector.

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4 r=⟨ ,…

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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: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4

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Q: Find a vector v parallel to the intersection of the planes - (x + 3y + 4z) = 7 and 2y – 2x + 2z = 7.…

A: The direction vector of the line of intersection of two planes is parallel to the cross product of…

Q: s the vector ở = (-1,–2,3) perpendicular to the plane 3x + 6y – 9z + 5 = 0? %3D

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Q: Verify that the two planes are parallel. -x + 6y + 3z = 4 1 - x + 2y + z = 5 3 Find the normal…

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Q: Find an equation of the plane passing through (0,-1,3) that is orthogonal to the planes 3x+4y-2z=0…

A: Let's find equation of the plane.

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 the scalar equation for the plane passing through the points P-(-1. 5.-1. P=(-1, 6, 5), and…

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Q: A normal vector for the plane 4x −2y + 7z−11 = 0 is ______.

A: We have given equation of plane  4x-2y+7z-11=0 Then, we  can write this as…

Q: Show that the point 1, - 2, 0 lies on both planes 3x-2y+z=7 and x-4y-2z=9. Hence, find the vector…

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Q: Verify that the two planes are parallel. -x + 6y + 3z = 2 -** + 2y + z = 3 Find the normal vector,…

A: We will use that if Ax+By+Cz=d is equation of plan than (A,B,C) is normal vector as well as…

Q: find the vector equation of a plane that contains the intersection line of x + y + z = 1 and x – y +…

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Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 5z + 10 =…

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Q: Find a scalar equation of the plane that contains the linex = 1 + t, y = 2 − t, z = 4 − 3tand is…

A: Given,The plane that contains the line x = 1 + t, y = 2 − t, z = 4 − 3t.So, we can say that the…

Q: Find an equation of the plane that passes through the point (3, 2, 2) and is perpendicular to the…

A: equation of the plane passing through the points (3, 2, 2)               A(x-3)+B(y-2)+C(z-2) = 0…

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: Find a nonzero vector parallel to the line of intersection of the two planes 5y – 4x + z =-1 and –…

A: The line of intersection of two planes is orthogonal to their respective normals.

Q: Verify that the two planes are parallel. -x + 6y + 3z = 6 1 -x + 2y + z = 7 Find the normal vector,…

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Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+y-2z = 3.

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Q: A normal vector for the plane 4x – 2y + 7z – 11 = 0 is

A: Solution is given below:

Q: generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then…

A: We know that equation of line through (x1,y1,z1)  and parallel to ai+bj+ck is

Q: Determine the scalar equation of the plane that passes through (5, -5, 5) and is perpendicular to…

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

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

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Q: Write the scalar equation of the plane with normal vector * - [3, 4, – 1] and passing through the…

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Q: Find the vector equation for the line of intersection of the planes 4x + 2y + 2z -1 and 4x + z= -2…

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Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 4 -*+ 3y + z = 5 Find the normal vector, n,,…

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 4y – 3x +3z = -2 and z…

A: Answer

Q: Find a nonzero vector parallel to the line of intersection of the two planes 5z – (3x+3y) : 2 and 2x…

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Q: perpendicular

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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.