If a plane contains two distinct points P1 and P2 then show that it contains every point on the line through P1 and P2.

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Given, through the point (4, 2, -5) and perpendicular to the plane…

Q: Determine an equation for the unique plane that passes through the points P(0,0, 2), Q(0,4, 0), and…

A: Given points are P(0,0,2), Q(0,4,0) and R(8,0,0). Find an equation for the unique plane that passes…

Q: Which of the points A(9, 0, 3), B(6, 5, 6), and C(2, 9, 2) is closest to the yz-plane? Which point…

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

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Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

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Q: Find the distance between line 1, and the plane parallel to it and containing line I, where 4:…

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Q: Find the distance (in appropriate units) between the points P(2,−1)P(2,−1)and Q(3,4)Q(3,4)in the…

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Q: 3. If a plane contains two distinct points Pi and P2 then show that it contains every point on the…

A: Solve the given

Q: Prove that the line x +1 = 글(-6) - lies in the plane 3x + y – 2 = 3.

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Q: The set of all points in a plane that are equidistant from a fixed line and fixed point is…

A: The set of all points in a plane that are equidistant from a fixed line and fixed point is a/an…

Q: The set of all points in a plane the sum of whose distances from two fixed points is constant is…

A: We have to fill the blanks The set of all points in a plane the sum of whose distances from two…

Q: Given the points F(8,4) and G(-7,-6) what are the coordinates of the point that partitions the…

A: Given that points are F8,4 and G−7,−6. We have to find the coordinates of the point that partitions…

Q: The planes x - 2y + 32 - 3 =0 and 3x + y - z + 5 =0 are perpendicular. Select one: True False

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Q: Determine the value of K such that the points A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,K,-2) lie on…

A: Given A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,k,-2) AB→=(0-4,(1+2),(0-6))=(-4,3,-6)…

Q: Find an equation for the plane through P(1,4, 4) that contains the line of intersection of the…

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Q: Find an equation of the plane consisting of all points that are equidistant from (0, -5, 2) and (-5,…

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Q: Find the distance from the point A(2,4,3) to the plane determined by the three points B(1,4,2),…

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Q: 30 0= +시 +씨 2 |and 3x-y-z=3 -8/

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Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

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Q: The set of all points in a plane that are equidistant from a fixed line and a fixed point is a/an…

A: Parabola is defined as a curve made up of all points that are equidistant from a fixed line and a…

Q: Find a plane containing the point (-3,3,-3) and the line F(t) = +t

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Q: Consider the line which passes through the point P(1, 3, -5), and which is parallel to the line æ =…

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Q: Find the equation of a plane consisting of all points that are equidistant from (5,5,-1) and…

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Q: 23. Through (1,3, 5) and normal to7 - } +k.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: In each case, determine whether or not the lines have a single point of intersection. If they do,…

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

A: Let the point P(x,y,z) be on the required plane which is equidistant from the given points (1, 0, 2)…

Q: Which of the points A(-4, 0, -1). B(3, 1, -1), and C(2, 4, 6) is closest to the yz-plane? Which…

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Q: For every two lines intersecting in space, there is only one plane in them True false

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Q: If l,, l2, and l3 are nonconcurrent lines, prove that there exist three points. Exactly one each…

A: Three or more points are said Lto be collinear if they all lie on the same straight line If l1 , l2…

Q: If the plane through the points P(1,1, –1),Q(3,0, 2), and R(-2,1,0), which of the following are…

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Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (-1,-6, 5)…

A: Given: Equation of line as, l:(x,y,z)=(-1,-6,5)+n(1,3,-2) And the equation of the plane is given as…

Q: Find and describe the intersection of the following line and plane: T:2x+3y-4z =-7 and r = (4,2,5)…

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Q: a). Determine a pair of planes whose intersection is the given line. = 2-3k, y = 3+e , Z- 2 -4€

A: Note: as per our guidelines we are supposed to answer only one question.* *Kindly repost other…

Q: Show that the line joining the points P(0,1,2) and Q(3,4,8) is parallel to the line joining the…

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Q: 3. If a plane contains two distinct points P1 and P2 then show that it contains every point on the…

A: The given problem can be proved both by mathematically and by the definition. For your convenience I…

Q: In triangular space it is sufficient to know two different points to find the line passing through…

A: Given statement is 'True'

Q: Show that the line joining the points P(0,1, 2) and Q(3, 4, 8) is parallel to the line joining the…

A: From the given problem:    L1:P0,1,2→x1,y1,z1Q3,4,8→x2,y2,z2   L2:R-2,32,-3→x1,y1,z1S52,6,6→x2,y2,z2…

Q: For Fano's geometry, prove that the lines through any one point of the geometry contain all the…

A: Given detail: For Fano's geometry, prove that the lines through any one point of the geometry…

Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (3,– 1, 7)…

A: Given: Parametric equation of line l: (x,y,z)=(3,-1,7)+r(-5,2,1) Equation of plane: 2x+3y+4z=24

Q: Prove that if P(I, y) be any point on the line segment joining R(11, Y1) and P2(12, Y2) then I= I1+…

A: Let P divides P1 and P2 in the ratio k : (1-k) x=kx2+1-kx1k+1-kx=kx2+x1-kx1x=x1+kx2-x1 Similarly…

Q: How can we recognize if the two planes were parallel or not

A: Consider the vector equation of the two given planes as, r→·n1→=d1r→·n2→=d2 Here, n1→ and n2→ are…

Q: Find a plane containing the point (2,-1,3) and the line of intersection of the planes 5x + 7y – 6z =…

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Q: 3. If a plane contains two distinct points P1 and P2 then show that it contains every point on the…

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Q: Find points in the Euclidean plane corresponding to the points e₁-[3,-5,-1], e2=[1,-2,2], e3 [2,1,0]…

A: By Pn , we denote the projective space of dimension n, defined as follows: Pn=Rn+1 \ {0}~, where '~'…

Q: ■ Find distance from point A(1,2,1) to the plane containing the three points B(2,2,4), C(-1, -2, -3)…

A: Distance of a point from plane