Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the plane with equation 6x + 5y + 8z = 3 Point= (, )

Q: Find the distance between the point (0,0,0) and the plane 2x – y + 2z = 4

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Q: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…

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Q: Find the distance from the point (3, 2, 5) to the plane whose general equation is 2x + 3y - z = 0.

A: we have to find the distance from the point (3,2,5) to the plane whose general equation is 2x+3y-z=0…

Q: Find distance from point (-6, 3, 5) to the plane – 2y – 4z = 8| -

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Q: Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the…

A: At the point of intersection the point will satisfy the equation of both line and the plane. So…

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with the xy-plane,…

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Q: write down the equation of the plane. The plane containing the point (1,-5,8) and orthogonal to the…

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Q: 9. Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

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Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

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Q: (6) Where does the line through (1,0, 1) and (4, -2, 2) intersect the plane r+y+ z = 6?

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

A: The parametric equations of the line x=3y=4z may be re-written as  so that its vector equation is…

Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, - 1, 2) is parallel | to the line x=…

A: Given that points are (2,1,-1), (0,-2,0) and (1,-1,2) The parametric equation is,…

Q: find the distance between point (-1,1,3) and the plane 5x-5y+3z=25

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Q: Find the distance between the point (1, 3, −1) and the plane 3x − 4y + 5z = 6.

A: According to the question, we have to find the distance between the points 1,3,-1and the plane…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

A: Find equation of line and put parametric value of (x,y,z) in plane and solve for x,y and z.

Q: Find an equation of the plane whose points are equidistant from (6, -5, 3) and (7,5, 5). 13x + 8z –…

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Q: Find a plane through the points P1(1, 2, 3), P2(3, 2, 1) and perpendicular to the plane 4x - y + 2z…

A: The given points and the plane are,

Q: 7. Find the distance between the point (- 3, 2, 1) and the plane with equation x - 2y + 3z = 5

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Q: Find the point of intersection of the lines 2t + 1, y = -t+ 2, z = t+ 1 and x 2s + 2, y = s+3,z =…

A: Given lines are x=2t+1, y=-t+2, z=t+1x=2s+2, y=s+3, z=5s+6

Q: Find the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…

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Q: Find the distance between the point (-1,–1,2) and the plane 2.x+5y-6z =4

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

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Q: The plane through the points (2, 1, –1), (0, –2, 0), and (1, – 1, 2) is parallel to the line x=1-t,…

A: Equation of plane passing through x1, y1, x2, y2, x3, y3 is given by,…

Q: Find the point of intersection of the line through (1, -5, 1) and (5,-12, 6), and the plane given by…

A: we know that equation of line which passes through two pointsx1,y1,z1,x2,y2,z2 is given by…

Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

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Q: int at which the line ⟨4,−1,−5⟩+t⟨−3,3,2⟩⟨4,−1,−5⟩+t⟨−3,3,2⟩ intersects the plane…

A: Given the line 4,-1,-5+t-3,3,2  intersects the plane -x+y+z=18.

Q: Find the distance between the point (0,0,0) and the plane 2x – y + 2z = 4.

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Q: 2. Obtain an equation for a plane 7 that includes straight line(2"--5) and point(-2,1,1).

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Q: Derermine the pointof intersection of the linel:- [-6,9,-1]+t[-a,3 ,1], t ER, and the plane, TT-x +…

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given the point (1,-3,1) and (3,-12,6) and the plane x-y+z=6

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

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Q: The line through the point (1, 0, 6) and perpendicular to the plane a + 3y + z = 5

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Q: Find the distance between (1,-2, - 1)and the plane through the points (1, 2, 3)and (3 , 2, 1)and…

A: Given information: The plane passes through the points (1, 2, 3) and (3 , 2, 1) and perpendicular to…

Q: What is the equation of the plane containing point (3,0,4) and orthogonal to the line WWWw…

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Q: 4. Determine the equation of the plane passing through the point (1, –4, 3) and parallel to x – y…

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Q: Find an equation ( in point - nomal form) of the plane containing the point (1.-3, 5) and the line…

A: Equation of a plane in point normal form is given as, A(x-a)+ B(y-b)+ C(z-c)=0 Where (A,B,C) is the…

Q: Find equation of the plane through (1,0,-1).(-1,2, 1) and parallel to the line of intersection of…

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Q: 4. Determine the equation of the plane passing through the point (1, -4, 3) and parallel to the…

A: We have to find an equation of the plane passing through the point (1, -4, 3) and parallel to the…

Q: 2. Obtain an equation for a plane a that includes straight line(2--5) and 1: point(-2,1,1)

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Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, -1, 2) is parallel to the line x 1-t,…

A: equation of plane for non collinear points , x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1 we will use…

Q: Find a plane containing the point (-7,-3,-2) and the line of intersection of the planes 3x – 2y – 3z…

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Q: Find the points of intersection of the line 6. = y+3= z 4 with the plane I+ 3y + 2z – 6 = 0. ОА(-10,…

A: We will solve the following.

Q: Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane…

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Q: Find an equation of a plane through the point (-2, 1, 5) which is orthogonal to the line 2= -3- 3t,…

A: The director vector of the line is (-3, -4, -3). Given that the plane is orthogonal to the line. So…

Q: Find a plane through the point Po(2, 1, -1) and perpendicular to the line of intersection of the…

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Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y -z = -2?

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Q: Are the plane 2x-y-4z 10 and the line {x = 2+4t,y 5- 2t,z =-8t} parallel or orthogonal?

A: We have to find out

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -8, 4), and the plane given by…

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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.