Exercise 6.9 In the Euclidean space: a) Find a plane passing through the points P = (1, 1, 1) and Q = (0, 1, 0), parallel to the x=y=0 line t of equations t: x + 2y = 1. b) Find a line r orthogonal to the plane and passing through P. c) Determine, if possible, a line s parallel to r and having distance 1 from r. How many lines have these properties? d) Determine, if possible, two lines satisfying the properties at c) and having distance equal to 2.

Q: Exercise 6.12 a) Write the cartesian equation of the plane orthogonal too: z-y+2z = 0 and containing…

A: Given: The given plane π is orthogonal to σ : x-y+2z=0 and contain the line  r : x+2y=3x-z=1

Q: ) a) Find the point at which the given lines intersect: b) Find an equation of the plane that…

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Q: State whether the following is true or false: g) The set of integers the usual metric is not…

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Q: 11. Consider the plane and the line with these equations: 0 = 2x + y -z + 10 a) :. e must b) Find…

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Q: Let A and B be the points defined by the position vectors a = 3i+j and b = 4i-2j, respectively.…

A: A and B be the points defined by the position vectots,To find,the shortest distance from A to the…

Q: Show that the lines L₁ : x = 1 -t, y = 2t, z = 5 + t and L₂: x=1+3t, y = 3-6t, z = 5-3t are parallel…

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Q: Q3: a) Find an equation for the plane through P(0,1,-2) perpendicular to n= 3i- 2j+k

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Q: Let A be the plane containing the points P(2,2,2), Q(2, 1,3 ) and R(3,1, 3) . (a) Find the equation…

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Q: Several friends chartered a boat for a day's fishing. They caught a total of 60 fish. The table…

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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: a) Find the point of intersection between the lines x = 2t, y =t+ 2, z = 3t – 1 x = 5k – 2, y = k+…

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Q: 2. Consider the following three points (a) (b) ( (c) P= (1, -3,1), Q = (2, 1,0), R= (1,0,1) Find the…

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Q: Let a be a real number such that a opposit to 0 . An equation of the plane passing through A…

A: Given data:- Plane passing through the points, Aa,-a,-aBa,0,2aC-a,-a,-5a

Q: Consider two lines in space: L1: x = 1-t, y = 2+ 3t, z = t and L2:3 a) Show that the lines are…

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Q: The third question: Let (1-, 1-, 1-) Q be a point in space and let us have the line L whose equation…

A: Let the equation of the plane passing through the point Q-1,-1,-1 be ax+1+by+1+cz+1=0…

Q: Consider the points K(−1, 0, 7) and M(1, −2, 5), the vector MN = , and the line L with symmetric…

A: The dot product of two vectors includes the cosine of the angle between them. When the two vectors…

Q: a) Find an equation of the plane passing through the points P=(1,–2,0),Q=(3,1,4) and R = (0, –1,2).

A: Given points are P1,−2,0, Q3,1,4, R0,−1,2. We have to find the equation of the plane passing through…

Q: Exercise 6.12 a) Write the cartesian equation of the plane orthogonal too: x-y+2z = 0 and containing…

A: The given plane π is orthogonal to σ : x-y+2z=0 and contain the line  r : x+2y=3x-z=1

Q: a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4] b) Find the…

A: Here we are solving part c.