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JEE MATHEMATICS MCQ: 3D GEOMETRY SYSTEM

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The point moves such that the area of the triangle formed by it with the points (1, 5) and (3,-7) is 21 sq unit. The locus of the point is
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Correct option: A
6x+y−32=06x + y - 32=0
Option A (6x+y−32=06x + y - 32=0) is correct because it represents the locus of the point derived from the area of the triangle formed by the given points.

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The mid point of the line joining the points (−10,  8)\left( { - 10,\;8} \right) and (−6,  12)\left( { - 6,\;12} \right) divides the line joining the points (4,  −2)\left( {4,\; - 2} \right) and (−2,  4)\left( { - 2,\;4} \right) in the ratio The equation of the plane perpendicular to the yzy z-plane and passing through the points (1,−2,4)(1,-2,4) and (3,−4(3,-4, 5)5) is The value of pp for which the lines 2x+y−3=02 x+y-3=0, 3x−y−2=03 x-y-2=0 and x−py+5=0x-p y+5=0 may intersect at a point is If the vertices of a triangle at O(0,0),A(a,0)O\left( {0,0} \right),A\left( {a,0} \right) and B(0,a).B\left( {0,a} \right). Then, the distance between its circumcentre and orthocentre is The coordinates of the foot of the perpendicular drawn from the point A(1,0,3)A(1,0,3) to the join of the points B(4,7,1)B(4,7,1) and C(3,5,3)C(3,5,3) are The area of the triangle formed by the three lines x1=y2=z3,x2=y1=z3\frac{x}{1}=\frac{y}{2}=\frac{z}{3}, \frac{x}{2}=\frac{y}{1}=\frac{z}{3} and x−11=2−y2,z=3\frac{x-1}{1}=\frac{2-y}{2}, z=3 is
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