In the space A³, consider the points P(-1,0,-1) and Q(2,0,-3) and the line 2x+3y +3z + 1 = 0 8 Write the parametric and cartesian equations of the liner passing through P and Q. Determine all the planes passing through P and Q and having the least possible dis- tance from s. Determine all the planes passing through P and Q and having the maximum possible distance from s.

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: Find an equation of the plane containing the three points P(1,2,2), Q(2,-1,4), and R(3,5,-2).

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Q: A city is described parametrically by the equation r = (ai + bj+ck) + svi + tv₂ where v₁ = 3i+j+ k…

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Q: Find an equation for the plane containing the three points (0, 1, -1), (1,0,1), and (2, 1, 0). Where…

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Q: check if the given vectors are linearly independent or not . {(-1, 1, 0), (-1, 0, 1), (1, 1, 1)}.…

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Q: :Find the equation of the plane through (-1, 6, 2) and perpendi cular to the jain of (1, 2, 3) and…

A: Given,           The equation of the pane through -1,6,1 and perpendicular to the join            of…

Q: Write the equation of the locus of a point whose distance from the plane 3x-2y-6z=12 is always twic…

A: We have to find the locus of the point P with the relation as per the distances given.

Q: Solve for z: 2²-(3-2)=(57-5).

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Q: ind the distance between the point (-1, 2, 1) and the plane 2x + 3y - 4z = 7. OTE: Give your answer…

A: Given query is to find the distance between the point and the plane.

Q: You are given the following points: A=(−4,20,16)A=(−4,20,16), B=(20,0,7)B=(20,0,7),…

A: Given- (x,y,z) coordinates of three points :A =(-4,20,16) B=(20,0,7) C=(8,-15,-19) to find- closest…

Q: 2) Find an equation of the plane that contains all points that are equidistant from the points…

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