Distance and Image of a Point from a Plane
Three Dimensional Geometry

121356 The distance of the point \((3,4,5)\) from the point of intersection of the line \(\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}\) and plane \(x+y+z=2\) is

1 13 units
2 10 units
3 7 units
4 6 units
Three Dimensional Geometry

121359 The distance of a point \((1,2,-1)\) from the plane \(\mathbf{x}-\mathbf{2 y}+\mathbf{4 z}+\mathbf{1 0}=\mathbf{0}\) is

1 \(\frac{\sqrt{3}}{7}\) units
2 \(\sqrt{\frac{7}{3}}\) units
3 \(\frac{3}{\sqrt{7}}\) units
4 \(\sqrt{\frac{3}{7}}\) units
Three Dimensional Geometry

121360 The length of the perpendicular from the point \((1,2,3)\) on the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}\) is

1 3 units
2 4 units
3 5 units
4 7 units
Three Dimensional Geometry

121362 Image point of \((1,3,4)\) in the plane \(2 x-y+z+\) \(\mathbf{3}=\mathbf{0}\) will be

1 \((3,5,2)\)
2 \((3,5,-2)\)
3 \((-3,5,2)\)
4 None of these
Three Dimensional Geometry

121363 The distance of the point \((1,-2,3)\) from the plane \(x-y+z=5\) measured parallel to the line \(\overrightarrow{\mathbf{r}}=(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})+\mathbf{t}(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-6 \hat{\mathbf{k}})\) will be

1 1
2 \(\frac{1}{7}\)
3 \(\frac{2}{7}\)
4 \(\frac{3}{7}\)
Three Dimensional Geometry

121356 The distance of the point \((3,4,5)\) from the point of intersection of the line \(\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}\) and plane \(x+y+z=2\) is

1 13 units
2 10 units
3 7 units
4 6 units
Three Dimensional Geometry

121359 The distance of a point \((1,2,-1)\) from the plane \(\mathbf{x}-\mathbf{2 y}+\mathbf{4 z}+\mathbf{1 0}=\mathbf{0}\) is

1 \(\frac{\sqrt{3}}{7}\) units
2 \(\sqrt{\frac{7}{3}}\) units
3 \(\frac{3}{\sqrt{7}}\) units
4 \(\sqrt{\frac{3}{7}}\) units
Three Dimensional Geometry

121360 The length of the perpendicular from the point \((1,2,3)\) on the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}\) is

1 3 units
2 4 units
3 5 units
4 7 units
Three Dimensional Geometry

121362 Image point of \((1,3,4)\) in the plane \(2 x-y+z+\) \(\mathbf{3}=\mathbf{0}\) will be

1 \((3,5,2)\)
2 \((3,5,-2)\)
3 \((-3,5,2)\)
4 None of these
Three Dimensional Geometry

121363 The distance of the point \((1,-2,3)\) from the plane \(x-y+z=5\) measured parallel to the line \(\overrightarrow{\mathbf{r}}=(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})+\mathbf{t}(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-6 \hat{\mathbf{k}})\) will be

1 1
2 \(\frac{1}{7}\)
3 \(\frac{2}{7}\)
4 \(\frac{3}{7}\)
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Three Dimensional Geometry

121356 The distance of the point \((3,4,5)\) from the point of intersection of the line \(\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}\) and plane \(x+y+z=2\) is

1 13 units
2 10 units
3 7 units
4 6 units
Three Dimensional Geometry

121359 The distance of a point \((1,2,-1)\) from the plane \(\mathbf{x}-\mathbf{2 y}+\mathbf{4 z}+\mathbf{1 0}=\mathbf{0}\) is

1 \(\frac{\sqrt{3}}{7}\) units
2 \(\sqrt{\frac{7}{3}}\) units
3 \(\frac{3}{\sqrt{7}}\) units
4 \(\sqrt{\frac{3}{7}}\) units
Three Dimensional Geometry

121360 The length of the perpendicular from the point \((1,2,3)\) on the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}\) is

1 3 units
2 4 units
3 5 units
4 7 units
Three Dimensional Geometry

121362 Image point of \((1,3,4)\) in the plane \(2 x-y+z+\) \(\mathbf{3}=\mathbf{0}\) will be

1 \((3,5,2)\)
2 \((3,5,-2)\)
3 \((-3,5,2)\)
4 None of these
Three Dimensional Geometry

121363 The distance of the point \((1,-2,3)\) from the plane \(x-y+z=5\) measured parallel to the line \(\overrightarrow{\mathbf{r}}=(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})+\mathbf{t}(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-6 \hat{\mathbf{k}})\) will be

1 1
2 \(\frac{1}{7}\)
3 \(\frac{2}{7}\)
4 \(\frac{3}{7}\)
Three Dimensional Geometry

121356 The distance of the point \((3,4,5)\) from the point of intersection of the line \(\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}\) and plane \(x+y+z=2\) is

1 13 units
2 10 units
3 7 units
4 6 units
Three Dimensional Geometry

121359 The distance of a point \((1,2,-1)\) from the plane \(\mathbf{x}-\mathbf{2 y}+\mathbf{4 z}+\mathbf{1 0}=\mathbf{0}\) is

1 \(\frac{\sqrt{3}}{7}\) units
2 \(\sqrt{\frac{7}{3}}\) units
3 \(\frac{3}{\sqrt{7}}\) units
4 \(\sqrt{\frac{3}{7}}\) units
Three Dimensional Geometry

121360 The length of the perpendicular from the point \((1,2,3)\) on the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}\) is

1 3 units
2 4 units
3 5 units
4 7 units
Three Dimensional Geometry

121362 Image point of \((1,3,4)\) in the plane \(2 x-y+z+\) \(\mathbf{3}=\mathbf{0}\) will be

1 \((3,5,2)\)
2 \((3,5,-2)\)
3 \((-3,5,2)\)
4 None of these
Three Dimensional Geometry

121363 The distance of the point \((1,-2,3)\) from the plane \(x-y+z=5\) measured parallel to the line \(\overrightarrow{\mathbf{r}}=(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})+\mathbf{t}(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-6 \hat{\mathbf{k}})\) will be

1 1
2 \(\frac{1}{7}\)
3 \(\frac{2}{7}\)
4 \(\frac{3}{7}\)
Three Dimensional Geometry

121356 The distance of the point \((3,4,5)\) from the point of intersection of the line \(\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}\) and plane \(x+y+z=2\) is

1 13 units
2 10 units
3 7 units
4 6 units
Three Dimensional Geometry

121359 The distance of a point \((1,2,-1)\) from the plane \(\mathbf{x}-\mathbf{2 y}+\mathbf{4 z}+\mathbf{1 0}=\mathbf{0}\) is

1 \(\frac{\sqrt{3}}{7}\) units
2 \(\sqrt{\frac{7}{3}}\) units
3 \(\frac{3}{\sqrt{7}}\) units
4 \(\sqrt{\frac{3}{7}}\) units
Three Dimensional Geometry

121360 The length of the perpendicular from the point \((1,2,3)\) on the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}\) is

1 3 units
2 4 units
3 5 units
4 7 units
Three Dimensional Geometry

121362 Image point of \((1,3,4)\) in the plane \(2 x-y+z+\) \(\mathbf{3}=\mathbf{0}\) will be

1 \((3,5,2)\)
2 \((3,5,-2)\)
3 \((-3,5,2)\)
4 None of these
Three Dimensional Geometry

121363 The distance of the point \((1,-2,3)\) from the plane \(x-y+z=5\) measured parallel to the line \(\overrightarrow{\mathbf{r}}=(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})+\mathbf{t}(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-6 \hat{\mathbf{k}})\) will be

1 1
2 \(\frac{1}{7}\)
3 \(\frac{2}{7}\)
4 \(\frac{3}{7}\)