1. Let L be the line given by the equation L: and S be the plane given by the equation S: 3r - 4y + 5z = 2 Find a scalar equation for the plane that contains the line L and is perpendicular to the plane

Q: Find an equation for the plane that passes through the point (-7, 10, –8), is parallel to the line x…

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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: Consider three points in three-dimensional space: А %3 (15, 2, —3), В %3 (2, —3, 15), С %3 (-3, 15,…

A: we know plane equation is <x-a, y-b, z-c>.n=0

Q: d an equation for the plane that passes through the origin and is perpendicular to the line (t) =…

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Q: Let P(3,-1,4) and Q(10, 13,9) u = (2,5, -1) and v= (7,-1,2) l be the line through P along direction…

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Q: Give an equation of the plane determined by the intersecting lines L1 and L2 L1 : x = 2t y = 4 – t z…

A: The equation of two lines is given as follows: L1: x=2t, y=4-t, z=3+t L2: x=2+s, y=-3+2s, z=s The…

Q: Engagement: Which One Doesn't Belong: Odd Line Out Which line doesn't belong? u

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Q: Find an equation for the line that is orthogonal to the plane 3x- y+ 2z =10 and goec through the…

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Q: Consider the plane with a scalar equation 4x-2y+z-19=0. Find the point of intersection of this plane…

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Q: The record showed that the number of students’ enrolment in a college is increasing by 5% per year.…

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Q: Consider the plane with equation 3x – 2y + 4z =7. A point has x coordinate 1 and y coordinate 2. If…

A: We have to find z coordinate

Q: Determine the equation of the plane that contains the lines Li and L2. L: x = 3- t, L2: x = 8 +2 s,…

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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: 3. Find the equation of the plane that includes the point (-1,0,7) and is parallel to the plane…

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Q: III. Consider the line ₁ given by the symmetric equations +1=-y-1 B 2 and the line ₂ given by 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: by the equations { L₁ : X Y Let L₁ and L2 be lines in a 3-dimensional space given { = = Z = 3 + 2t…

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Q: Give an equation of a plane described below. Determined by intersecting lines L1 and L2 L1: x = 2t y…

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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: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

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Q: You want to build a 1000 square foot rectangular infinity pool. Three of the sides will have regular…

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