Co-ordinate of a Point in Space
Three Dimensional Geometry

121095 The point dividing the join of \((3,-2,1)\) and \((-2,3,11)\) in the ratio \(2: 3\) is

1 \((1,1,4)\)
2 \((1,0,5)\)
3 \((2,3,5)\)
4 \((0,6,-1)\)
Three Dimensional Geometry

121096 A ray of light passing through the point \((1,2)\) reflects on the \(x\)-axis at point \(A\) and the reflected ray passes through the point \((5,3)\). The co-ordinate of \(A\) is

1 \(\left(\frac{5}{13}, 0\right)\)
2 \(\left(\frac{13}{5}, 0\right)\)
3 \(\left(\frac{-5}{13}, 0\right)\)
4 \(\left(\frac{-13}{5}, 0\right)\)
Three Dimensional Geometry

121097 If origin is the centroid of a triangle \(P Q R\) with vertices \(P(2 a, 2,6), \quad Q(-4,3 b,-10)\) and \(R(8,14,2 c)\), the value of \(a, b\) and \(c\) are respectively

1 \(-2,2,2\)
2 \(-2,2,-16 / 3\)
3 \(-2,-16 / 3,2\)
4 \(-16 / 3,-2,2\)
Three Dimensional Geometry

121098 The foot of perpendicular from \((5,7,3)\) to the line joining the points \((9,13,15)\) and \((12,21\), 10) is .....

1 \((-2,-19,7)\)
2 \((2,19,7)\)
3 \((2,2,3)\)
4 \((9,13,15)\)
Three Dimensional Geometry

121099 If the foot of the perpendicular drawn from the origin to a plane is \((1,2,3)\), then a point on that plane is

1 \((3,2,1)\)
2 \((7,2,1)\)
3 \((7,3,-1)\)
4 \((6,-3,4)\)
Three Dimensional Geometry

121095 The point dividing the join of \((3,-2,1)\) and \((-2,3,11)\) in the ratio \(2: 3\) is

1 \((1,1,4)\)
2 \((1,0,5)\)
3 \((2,3,5)\)
4 \((0,6,-1)\)
Three Dimensional Geometry

121096 A ray of light passing through the point \((1,2)\) reflects on the \(x\)-axis at point \(A\) and the reflected ray passes through the point \((5,3)\). The co-ordinate of \(A\) is

1 \(\left(\frac{5}{13}, 0\right)\)
2 \(\left(\frac{13}{5}, 0\right)\)
3 \(\left(\frac{-5}{13}, 0\right)\)
4 \(\left(\frac{-13}{5}, 0\right)\)
Three Dimensional Geometry

121097 If origin is the centroid of a triangle \(P Q R\) with vertices \(P(2 a, 2,6), \quad Q(-4,3 b,-10)\) and \(R(8,14,2 c)\), the value of \(a, b\) and \(c\) are respectively

1 \(-2,2,2\)
2 \(-2,2,-16 / 3\)
3 \(-2,-16 / 3,2\)
4 \(-16 / 3,-2,2\)
Three Dimensional Geometry

121098 The foot of perpendicular from \((5,7,3)\) to the line joining the points \((9,13,15)\) and \((12,21\), 10) is .....

1 \((-2,-19,7)\)
2 \((2,19,7)\)
3 \((2,2,3)\)
4 \((9,13,15)\)
Three Dimensional Geometry

121099 If the foot of the perpendicular drawn from the origin to a plane is \((1,2,3)\), then a point on that plane is

1 \((3,2,1)\)
2 \((7,2,1)\)
3 \((7,3,-1)\)
4 \((6,-3,4)\)
Three Dimensional Geometry

121095 The point dividing the join of \((3,-2,1)\) and \((-2,3,11)\) in the ratio \(2: 3\) is

1 \((1,1,4)\)
2 \((1,0,5)\)
3 \((2,3,5)\)
4 \((0,6,-1)\)
Three Dimensional Geometry

121096 A ray of light passing through the point \((1,2)\) reflects on the \(x\)-axis at point \(A\) and the reflected ray passes through the point \((5,3)\). The co-ordinate of \(A\) is

1 \(\left(\frac{5}{13}, 0\right)\)
2 \(\left(\frac{13}{5}, 0\right)\)
3 \(\left(\frac{-5}{13}, 0\right)\)
4 \(\left(\frac{-13}{5}, 0\right)\)
Three Dimensional Geometry

121097 If origin is the centroid of a triangle \(P Q R\) with vertices \(P(2 a, 2,6), \quad Q(-4,3 b,-10)\) and \(R(8,14,2 c)\), the value of \(a, b\) and \(c\) are respectively

1 \(-2,2,2\)
2 \(-2,2,-16 / 3\)
3 \(-2,-16 / 3,2\)
4 \(-16 / 3,-2,2\)
Three Dimensional Geometry

121098 The foot of perpendicular from \((5,7,3)\) to the line joining the points \((9,13,15)\) and \((12,21\), 10) is .....

1 \((-2,-19,7)\)
2 \((2,19,7)\)
3 \((2,2,3)\)
4 \((9,13,15)\)
Three Dimensional Geometry

121099 If the foot of the perpendicular drawn from the origin to a plane is \((1,2,3)\), then a point on that plane is

1 \((3,2,1)\)
2 \((7,2,1)\)
3 \((7,3,-1)\)
4 \((6,-3,4)\)
Three Dimensional Geometry

121095 The point dividing the join of \((3,-2,1)\) and \((-2,3,11)\) in the ratio \(2: 3\) is

1 \((1,1,4)\)
2 \((1,0,5)\)
3 \((2,3,5)\)
4 \((0,6,-1)\)
Three Dimensional Geometry

121096 A ray of light passing through the point \((1,2)\) reflects on the \(x\)-axis at point \(A\) and the reflected ray passes through the point \((5,3)\). The co-ordinate of \(A\) is

1 \(\left(\frac{5}{13}, 0\right)\)
2 \(\left(\frac{13}{5}, 0\right)\)
3 \(\left(\frac{-5}{13}, 0\right)\)
4 \(\left(\frac{-13}{5}, 0\right)\)
Three Dimensional Geometry

121097 If origin is the centroid of a triangle \(P Q R\) with vertices \(P(2 a, 2,6), \quad Q(-4,3 b,-10)\) and \(R(8,14,2 c)\), the value of \(a, b\) and \(c\) are respectively

1 \(-2,2,2\)
2 \(-2,2,-16 / 3\)
3 \(-2,-16 / 3,2\)
4 \(-16 / 3,-2,2\)
Three Dimensional Geometry

121098 The foot of perpendicular from \((5,7,3)\) to the line joining the points \((9,13,15)\) and \((12,21\), 10) is .....

1 \((-2,-19,7)\)
2 \((2,19,7)\)
3 \((2,2,3)\)
4 \((9,13,15)\)
Three Dimensional Geometry

121099 If the foot of the perpendicular drawn from the origin to a plane is \((1,2,3)\), then a point on that plane is

1 \((3,2,1)\)
2 \((7,2,1)\)
3 \((7,3,-1)\)
4 \((6,-3,4)\)
Three Dimensional Geometry

121095 The point dividing the join of \((3,-2,1)\) and \((-2,3,11)\) in the ratio \(2: 3\) is

1 \((1,1,4)\)
2 \((1,0,5)\)
3 \((2,3,5)\)
4 \((0,6,-1)\)
Three Dimensional Geometry

121096 A ray of light passing through the point \((1,2)\) reflects on the \(x\)-axis at point \(A\) and the reflected ray passes through the point \((5,3)\). The co-ordinate of \(A\) is

1 \(\left(\frac{5}{13}, 0\right)\)
2 \(\left(\frac{13}{5}, 0\right)\)
3 \(\left(\frac{-5}{13}, 0\right)\)
4 \(\left(\frac{-13}{5}, 0\right)\)
Three Dimensional Geometry

121097 If origin is the centroid of a triangle \(P Q R\) with vertices \(P(2 a, 2,6), \quad Q(-4,3 b,-10)\) and \(R(8,14,2 c)\), the value of \(a, b\) and \(c\) are respectively

1 \(-2,2,2\)
2 \(-2,2,-16 / 3\)
3 \(-2,-16 / 3,2\)
4 \(-16 / 3,-2,2\)
Three Dimensional Geometry

121098 The foot of perpendicular from \((5,7,3)\) to the line joining the points \((9,13,15)\) and \((12,21\), 10) is .....

1 \((-2,-19,7)\)
2 \((2,19,7)\)
3 \((2,2,3)\)
4 \((9,13,15)\)
Three Dimensional Geometry

121099 If the foot of the perpendicular drawn from the origin to a plane is \((1,2,3)\), then a point on that plane is

1 \((3,2,1)\)
2 \((7,2,1)\)
3 \((7,3,-1)\)
4 \((6,-3,4)\)