Consider the planes 5x+2y+4z=15x+2y+4z=1 and 5x+4z=0  (A) Find the unique point P on the y-axis which is on both planes ( .... ,...., ....) (B) Find a unit vector uu with positive first coordinate that is parallel to both planes.   .... i + .... j + .... k (C) Use parts (A) and (B) to find a vector equation for the line of intersection of the two planes  r(t)= .... i + .... j + .... k

Q: Find a vector parameterization of the plane 5x−4y−1z=18

A: By using prametrization

Q: Find the equation of a plane that is perpendicular to the vector 4 i + 2 j - 2 k and passing through…

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Q: 90. a. Determine the vector and parametric equations of the plane that passes through the points…

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Q: 3. Find the Scalar eguation of the plane containing the line rt) =<!,2,-37+ -3,2, 17 and the point…

A: Given problem:- Find the scalar equation plane containing the line  r (t)= &lt;1,2,-3 &gt; + t &lt;…

Q: 3 2) Determine the vector, parametric and cartesian eguation ef the line passing through-the…

A: Given: Passing point P0(1,3,2) Parallel vector V=(1,1,1)

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: Let ū = (0, 1, –1), v = (2, 1,0) and w = (4, 1, 1). a) Show that ū, ū and w lie in the same plane…

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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: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

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Q: 8. Find a vector parallel to the line of intersection of the two planes a – 2y + z = 1, 2x + y + z =…

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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: Consider the planes 5x + 3y + 5z = 1 and 5x + 5z =0 a) find the unique point p on the y-axis which…

A: given planes  5x + 3y + 5z = 1 and 5x + 5z =0

Q: (a) Find a vector parallel to the line of intersection of the planes 4x + 3y – 2z = -5 and -5x + y –…

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Q: Derive a parametric representation and find a normal vector for the plane 6x – 2y + 10z = 16. NOTE:…

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Q: 5. Show that lines l and lz intersect, find the point of intersection, then find a parametric…

A: Consider the provided question, Given that,l1: x,y,z=-3,1,5+t2,-2,1l2: x,y,z=13,-6,-2+s4,-1,-3 The…

Q: 1. Let II, be the plane passing through the point (7, 1,6), and that contains the line r(t) = (1,0,…

A: Given that π1 be the plane passing through the point (7,1,6), and that contains the line…

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 . &lt;x, y, z&gt; = d is said to be in normal form if n…

Q: What is equation of the plane passing through the point A(2, 1,3) and parallel to the vectors a = j-…

A: We have to find the equation of plane passing through point A(2,1,3) and parallel to vectors…

Q: snip1

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

Q: 1. Consider the plane II1 : 3z + 2y + x = 2. (a) If II2 : 2z – 3y = 1 is another plane. Are the…

A: Here we solve the three dimensional geometry problem.

Q: The planes I. and II, have equations IL : 6y+5z =-19, 5 II,: -x -4y+7z =1. State the normal vector…

A: We have to find the normal vectors of the given planes.

Q: 1. Let P(1, 1,-1), Q(1,2,0), and R(-1,0,0) be given points. Give the equation of the plane…

A: You are asked multiple questions. As per our guideline we can solve only one. Please repost the rest…

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

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Q: 5. (a) Consider the vectors u = (1,0, 1) and ē of the 2-dimensional parallelogram determined by…

A: we are given that

Q: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

A: SOLUTION-

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

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Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane - 6x + 8y – 10z - 4 = 0 are in…

A: We find out the results by using vectors in 3D

Q: Find a vector tangent to the curve of intersection of the two cyclinders ? + y² = 98 and y² + z² =…

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Q: . The line (x-2z 3, y 22) intersects the plane (x+3y-:+4=0) at the point P, Find: (a) the…

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Q: 2. Consider the points P = (3, 2, –1), Q = (-1,1, 1), and R = (-3,0, 2). %3D (a) Find parametric and…

A: Equation of plane

Q: a) Find the scalar parametric form of the equation of the line which is parallel to the line of…

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Q: Consider the line l in R³ given by the parametric vector equation 3 1 -2 -1 and the plane described…

A: Given that the line l in R3 given by the parametric vector equation and the plane described by the…

Q: 7. (a) What is the projection matrix that projects all vectors in R³ onto the plane x+ y + z = 0?…

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Q: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

A: According to question given thatplanes equation 4x-y-3z=6-5x+4y-4z=3

Q: (a) Find a vector n perpendicular to the plane z = 8x + 9y. (b) Find a vector v parallel to the…

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Q: 5. Show that lines lh and lz intersect, find the point of intersection, then find a parametric…

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Q: Consider the points P = (3,2, –1), Q = (-1,1,1), and R= (-3,0,2). %3D (a) Find parametric and…

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Q: The planes 3x−4y+5z=−28 and 4x−2y+4z=−24 are not parallel, so they must intersect along a line that…

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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: Find a scalar equation of the plane that passes through the points (1, 1, 1) and (2,0,3) and is…

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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: 4. (8 points) Find a vector parametrization for the intersection of the plane x +y+z = 3 and the…

A: Use polar coordinates for Parameterization

Q: (a) Find a vector parallel to the line of intersection of the -2. 3y - 4z planes -x + 3y + 4z = 0…

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Q: Find the equation for the plane through the point Po = (8,4,8) and normal to the vector n=2i + 2j +…

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Q: The Cartesian equation of the straight line tangent to the plane curve given parametrically by the…

A: Explanation of the answer is as follows

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: Find a vector parallel to the line of intersection of the planes 4х + 2y - 33 %3D17 and 3x - 4y…

A: Vector parallel to the Inter section of two planes  a and b is cross product of a and b Let m is a…

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.