Given: The vertices of a triangle are \[A\text{ }\left( 1,\text{ }2,\text{ }3 \right),\text{ }B\text{ }\left( 0,\text{ }4,\text{ }1 \right),\text{ }C\text{ }\left( -1,\text{ }-1,\text{ }-3 \right)\]...
Given: The mid-points of the sides of a triangle \[ABC\] is given as \[\left( -2,\text{ }3,\text{ }5 \right),\text{ }\left( 4,\text{ }-1,\text{ }7 \right)\text{ }and\text{ }\left( 6,\text{ }5,\text{...
Given: The points \[\left( 2,\text{ }-1,\text{ }3 \right)\text{ }and\text{ }\left( -1,\text{ }2,\text{ }1 \right)\] By using the section formula, Let \[C\left( x,\text{ }y,\text{ }z \right)\]be any...
Given: The points \[\left( 2,\text{ }4,\text{ }5 \right)\text{ }and\text{ }\left( 3,\text{ }5,\text{ }4 \right)\] By using the section formula, We know X coordinate is always 0 on yz-plane So, let...
Given: The points \[A\text{ }\left( 2,\text{ }3,\text{ }4 \right),\text{ }B\text{ }\left( -1,\text{ }2,\text{ }-3 \right)\text{ }and\text{ }C\text{ }\left( -4,\text{ }1,\text{ }-10 \right)\] By...
Given: The points \[A\text{ }\left( 2,\text{ }-3,\text{ }4 \right)\text{ }and\text{ }B\text{ }\left( 8,\text{ }0,\text{ }10 \right)\] By using the section formula, Let Point \[C\left( x,\text{...
Given: The vertices of the triangle are \[A\text{ }\left( 5,\text{ }4,\text{ }6 \right),\text{ }B\text{ }\left( 1,\text{ }-1,\text{ }3 \right)\text{ }and\text{ }C\text{ }\left( 4,\text{ }3,\text{ }2...
Given: The points \[A\text{ }\left( 1,\text{ }3,\text{ }4 \right),\text{ }B\text{ }\left( -1,\text{ }6,\text{ }10 \right),\text{ }C\text{ }\left( -7,\text{ }4,\text{ }7 \right)\] and \[D\text{...
Given: The points \[A\text{ }\left( 1,\text{ }3,\text{ }0 \right),\text{ }B\text{ }\left( -5,\text{ }5,\text{ }2 \right),\text{ }C\text{ }\left( -9,\text{ }-1,\text{ }2 \right)\] and \[D\text{...
Given: The points \[A\left( 3,3,3 \right),B\left( 0,6,3 \right),C\left( 1,7,7 \right)\text{ }and\text{ }D\left( 4,4,7 \right)\] We know that all sides of a square are equal. By using the formula,...
Given: The points \[\left( 0,\text{ }7,\text{ }10 \right),\text{ }\left( -1,\text{ }6,\text{ }6 \right)\text{ }and\text{ }\left( -4,\text{ }9,\text{ }6 \right)\] Isosceles right-angled triangle is a...
Given: The points \[\left( 1,\text{ }2,\text{ }3 \right),\text{ }\left( 2,\text{ }3,\text{ }1 \right)\text{ }and\text{ }\left( 3,\text{ }1,\text{ }2 \right)\] An equilateral triangle is a triangle...
Given: The point \[\left( 1,\text{ }2,\text{ }3 \right)\] Distance \[=\text{ }\surd 21\] We know \[x\text{ }=\text{ }0\text{ }and\text{ }y\text{ }=\text{ }0\] on z-axis Let \[R\left( 0,\text{...
Given: The points \[\left( 3,\text{ }1,\text{ }2 \right)\text{ }and\text{ }\left( 5,\text{ }5,\text{ }2 \right)\] We know \[x\text{ }=\text{ }0\text{ }and\text{ }z\text{ }=\text{ }0\] on y-axis Let...
Given: The points \[\left( 1,\text{ }5,\text{ }7 \right)\text{ }and\text{ }\left( 5,\text{ }1,\text{ }-4 \right)\] We know \[x\text{ }=\text{ }0\text{ }and\text{ }y\text{ }=\text{ }0\text{ }on\text{...
\[zx-plane\] We know \[y\text{ }=\text{ }0\text{ }in\text{ }xz-plane\] Let \[R\left( x,\text{ }0,\text{ }z \right)\] any point in \[xz-plane\] According to the question: \[RA\text{ }=\text{...
Given: The points \[A\left( 1,\text{ }-1,\text{ }0 \right),\text{ }B\left( 2,\text{ }1,\text{ }2 \right)\text{ }and\text{ }C\left( 3,\text{ }2,\text{ }-1 \right)\] (i) \[xy-plane\] We know \[z\text{...
(i) \[A\left( 3,\text{ }-5,\text{ }1 \right),\text{ }B\left( -1,\text{ }0,\text{ }8 \right)\text{ }and\text{ }C\left( 7,\text{ }-10,\text{ }-6 \right)\] Given: The points \[A\left( 3,\text{...
(i) \[A\left( 4,\text{ }-3,\text{ }-1 \right),\text{ }B\left( 5,\text{ }-7,\text{ }6 \right)\text{ }and\text{ }C\left( 3,\text{ }1,\text{ }-8 \right)\] Given: The points \[A\left( 4,\text{...
Given: The points \[\left( -2,\text{ }3,\text{ }1 \right)\text{ }and\text{ }\left( 2,\text{ }1,\text{ }2 \right)\] By using the formula, The distance between any two points \[\left( a,\text{...
(i) \[P\left( 1,\text{ }-1,\text{ }0 \right)\text{ }and\text{ }Q\text{ }\left( 2,\text{ }1,\text{ }2 \right)\] Given: The points \[P\left( 1,\text{ }-1,\text{ }0 \right)\text{ }and\text{ }Q\text{...
Given: Point \[\left( 3,\text{ }-2,\text{ }5 \right)\] The Absolute value of any point \[\left( x,\text{ }y,\text{ }z \right)\] is given by, \[\surd ({{x}^{2}}~+\text{ }{{y}^{2}}~+\text{...
Given: The point \[P\text{ }\left( -4,\text{ }3,\text{ }5 \right)\] The distance of the point from x-axis is given as: The distance of the point from y-axis is given as: The distance of the point...
Given: Points are \[\left( 5,\text{ }0,\text{ }2 \right)\text{ }and\text{ }\left( 3,\text{ }-2,\text{ }5 \right)\] We need to find the lengths of the edges of the parallelepiped formed For point...
Given: Points are \[\left( 3,\text{ }0,\text{ }-1 \right)\text{ }and\text{ }\left( -2,\text{ }5,\text{ }4 \right)\] We need to find the lengths of the edges of the parallelepiped formed. For point...
Given: A cube has side \[4\]having one vertex at \[\left( 1,\text{ }0,\text{ }1 \right)\] Side of cube \[=\text{ }5\] We need to find the coordinates of the other vertices of the cube. So let the...
\[\left( -4,\text{ }0,\text{ }0 \right)\] Since we need to find its image in \[xy-plane,\] sign of its \[z-coordinate\]will change So, Image of point \[\left( -4,\text{ }0,\text{ }0 \right)\text{...
(i) \[\left( 5,\text{ }2,\text{ }-7 \right)\] Since we need to find its image in \[xy-plane,\] a sign of its \[z-coordinate\] will change So, Image of point \[\left( 5,\text{ }2,\text{ }-7...
(i) \[\left( -2,\text{ }3,\text{ }4 \right)\] Since we need to find its image in \[yz-plane,\] a sign of its \[x-coordinate\]will change So, Image of point \[\left( -2,\text{ }3,\text{ }4...
(i) \[\left( 2,\text{ }-5,\text{ }-7 \right)\] In this case, since \[z\text{ }and\text{ }y\] are negative and \[x\] is positive then the octant will be \[XOY\prime Z\prime \] (ii) \[\left( -7,\text{...
(i) \[\left( -5,\text{ }-4,\text{ }7 \right)\] In this case, since \[x\text{ }and\text{ }y\]are negative and \[z\]is positive then the octant will be \[X\prime OY\prime Z\] (ii) \[\left( -5,\text{...
(i) \[\left( 4,\text{ }-3,\text{ }5 \right)\] In this case, since \[y\]is negative and \[x\text{ }and\text{ }z\] are positive then the octant will be \[XOY\prime Z\] (ii) \[\left( 7,\text{ }4,\text{...
(i) \[\left( 5,\text{ }2,\text{ }3 \right)\] In this case, since \[x,\text{ }y\text{ }and\text{ }z\] all three are positive then octant will be \[XOYZ\] (ii) \[\left( -5,\text{ }4,\text{ }3...