) Find the locus of a point, - z = 0, x 2y + z - the sum of squares of whose distances from the 6 and x + y + z = 1 is 36 ) A ray of light passing through the point 4(1,2,3), strikes the plane x + y 8 and on reflection passes through point C(3, 5, 9). Find the coordinates o ) Find the radius of the circular section in which the sphere vec | r | = 5 cut r. (i+j+ k) = 3√√3

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: (0,1,1) to the line of intersection of the planes : x + 2y + z = 1 x - y + 2z = -8

A:

Q: findthe parametríc equatlons for the line through the paint of in tersecti of the lines 4=X=2+ 36 14…

A: first we find intersection point of given line

Q: X Edit 10. Rectangle GHU wilth verlices G(2.-1), H7.-1), 17.-4), and

A: Graph plotting

Q: Q. (a) Find an equation of the tangent plane to each surface at the given point. (b) Find symmetric…

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Q: A solid concrete porch consists of 3 steps and a landing. The steps have a tread of 11 inches, a…

A:

Q: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: You are given the following points: A = (11,20, –-18), B= (19,0,3), C =(-7,10,14). Which point is…

A:

Q: e) Plane that is parallel to the xy-plane that contains the point A(2, 1, 3) (ca

A:

Q: 19. Find the Cartesian equation of the plane a) passes through point A(6,- 7, 4) and parallel to the…

A: To find the Cartesian equation of the plane, a)Which passes through the point A6,-7,4 and parallel…

Q: ind the equation of the tongent plane to fox,y)=x²-2xy + 2y ² slope 2 in the positive x direction…

A:

Q: Q4) Find the intersection of the line x = and the sphere x? + (y – 3)² + (z – 2)² = 4. A) (1,1,0) B)…

A: 1. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all…

Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

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Q: b) Let l and l2 be lines in 3 space such that 2. 4 passes through the point with coordinates (3, 4,…

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Q: y -1 Q2) L, =Xx2 = -1 - 2 Fand equation of plane Canternng them

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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: (10) Find the distance of (3,-1,2) from each of the following: a) line: x = 1+ 2t, y = -t, z = 1-t…

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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: (9) (a) Find the point P on the plane ry+2=-3 that is closest to the point Q(2, 3, 4). Is the point…

A: