Find the point of intersection of the lines 2t + 1, y = -t+ 2, z = t+ 1 and x 2s + 2, y = s+3,z = 5s+ 6 and then the plane determined by these lines.

Q: The plane passes through the point (18, -16, 9) and contains the line given by = = z . 1.

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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 vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

Q: Find the plane determined by the intersecting lines. z = 1-t L1 x= - 1 +t y = 2 + 3t L2 x = 1- 4s y…

A: Given: L1  x=-1+t    y= 2+3t   z=1-tL2  x=1-4s   y=1+2s   z=2-2s To find equation of  plane by these…

Q: Calculate the equation of the line that passes through the point (0, 1, 2) that is parallel to the…

A: We need to find the equation of the line passing through a point, parallel to a plane and…

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: Find an equation of the plane. The plane that passes through the point (1, -1, 1) and contains the…

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

A: It can be assumed that the vector for the coordinate 1,0,1 is 1,0,1 and the vector for the…

Q: Find an equation of the plane containing (1, 5, -1) that is perpendicular to the line of…

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Q: find the equation of the plane passing through(1,0,-1)&(-1,2,1) and parallel to the line of…

A: To determine: The equation of the plane passing through the points (1, 0, -1) and (-1, 2, 1) and…

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

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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 the point-normal form equation of the plane containing the point (1, -3, 5) and the line with…

A: Solution: P(1 , -3 , 5) (2 - x ) = (y+1)/2 = -z/3 = t

Q: Give the general equation of a plane which has point (1,2, -1) together with line with symmetric…

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

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Q: Find a plane containing the point (- 5, – 5, 2) and the line r (t) = (1, – 2, 1) + t(4, 7, 5).

A: Given that the required plane passes through the point P=(-5,-5,2) and required plane contains the…

Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x = −6+t,…

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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 point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

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Q: Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x – y + z = 2…

A: For solving This question I found direction cosine using dot product as two perpendicular plane is…

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: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y- 2z=3 is: *

A: Plan 1: 4x-y+z=2 Plan 2: 2x+y+2z=3

Q: Find an equation of the plane through (1,8, 5) that is perpendicular to the line x – 2 = 3t, y + 3 =…

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Q: What is the equation of the plane through the point (4, -2, 3) and parallel to the plane 3x - 7z =…

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Q: Find the equation of the plane that contains both of the lines given below. Line 1: x = 1+t, y = 2+…

A: Line 1 : x=1+t, y=2+2t, z=3-t        ⇒a⇀=1, 2, 3, l⇀=1, 2, -1 Line 2 : x=1-s, y=2+4s, z=3+2s…

Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

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

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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 intersection point of the line whose equation is (x+2y+z=1),(x+y+2z=-1) with the xz plane is: O…

A: Here the two equation are: x+2y+z=1x+y+2z=-1

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: To find the intersecting point, we substitute the values of x, y, and z in the equation of plane and…

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

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Q: Write the equation of the plane passing through point (3, 8, 3) that is parallel to the xz-plane.. X…

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Q: find the equation of the plane passing through (1,0,-1)&(-1,2,1) and parallel to the line 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: Find an equation of the plane orthogonal to the line (z, y, 2) = (-1, 10, –-10) +t (4, –9, -4) which…

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Q: Find the point at which the line (0, –3, 5) + t(4, –1,2) intersects the plane 4x + 4y – 4z = 0.

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Q: Write the equation of the plane passing through point (3, 8, 3)| that is parallel to the xz- plane..

A: Given: A plane passes through (3, 8, 3) and is parallel to the xz-plane. To Find: Equation of plane

Q: Find a plane containing the point ( - 5, - 5, 2) and the line r(t) = (1, - 2, 1) + t(4, 7, 5).

A: First you will find the normal vector to the plane and then find the value of the constant d

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

A: Given : the equation of a plane is  x-y+z=5  and the line passes through (1, -4, 1)  and (4, -10,…

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 the plane determined by the intersecting lines. y = 2+ 4t L1 x= - 1+2t z = 1- 2t L2 x= 1-4s y =…

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

A: Find the equation of line and then find its intersection with the plane

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