34) Show there is no plane perpendicular to n= î +î that passes through points P(1, 2, 3) and Q(2,3, 4)

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 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: What is the distance of the origin to the plane through (√3, √3,0), (√3,0, √3) and (0,√3,√3).

A: We have to find the distance of the origin to the plane passing through  and .

Q: Q10)The two lines L1: x=3-2t, y=4+t ,z= 6-t and L2: x=5-4t, .y=-2+2t, z=7-2t are parallel

A: 10) The equation of the line x=3-2t t=x-3-2 y=4+t t=y-4 z=6-t t=z-6-1

Q: 2) = ( (x, y, z) =

A:

Q: Find the equation of the plane that contains the line x = 1+t, y = 2+2t, z = 3- (1, -2,4). e point p…

A:

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

A:

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: 22Prove that the line X2l+2t y=ー+3t そ2 :2+4t is s perpendicular tou the plane X-2yrzz6

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Q: Find the distance between the parallel lines in each pair. a) l₁: [x, y, z] = [2, 5, 4] + [2, 1, 3]…

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Q: 13) Find the equation in slope-intercept form that is tangent to (x- 1)² + (y + 2)² = 25 and passes…

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Q: Find a plane containing the point (2,2,-5) and the line r(t) =<-6, -3, -7 > + < 6, -6,1…

A: Steps are explained in the image:

Q: 4. Using two methods find the point point P = (5, 4, 4) on the plane x +y + z = 4 nearest the %3D

A:

Q: 19. The plane through (3, -1, 1), (4, 0, 2), and (6, 3, 1) Answer + -4x + 3y + z = -14

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Q: - ARŞT is drawn on the coordinate plane. The coordinates of R are (0, 6). The coordinates of S are…

A: We need to find the third coordinate of triangle such that the area is 6 sq units.

Q: Prove that three points P(5,-4), Q(-3,8) and R(1,2) on the rectangular coordinate plane are…

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

A: Let the equation of the plane that contains the line of intersection of the planes 3x-y+3z=-1 and…

Q: 10. The distance between the point (3,-2,5) and the plane 2x+2y+z=5 is NONE

A: Given: The distance between (3,-2,5) and the plane 2x+2y+z=5

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

Q: A plane through the three points P = (4, -3, 5), Q = (-2, -3, 5), and R= (-2, 3, -3) is described by…

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Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: the

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Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

A: