87671 If \(P(1,2,3), R(4,5,-1)\) are the vertices and \(G(2,3,-1)\) is the centroid of \(\triangle P Q R\), then coordinates of midpoint of \(P Q\) are

87672 If \(A, B, C\) and \(D\) are \((3,7,4),(5,-2,3),(-4,5,6)\) and \((1,2,3)\) respectively, then the volume of the parallelopiped with \(A B, A C\) and \(A D\) as the coterminus edges, is (in cubic units)

87673 If \(\mathbf{G}(3,-5, r)\) is centroid of triangle \(A B C\) where \(A(7,-8,1), B(p, q, 5)\) and \(C(q+1,5 p, 0)\) are vertices of a triangle then values of \(p, q, r\) are respectively

87674 If \(\mathbf{G}(\overrightarrow{\mathbf{g}}), \mathbf{H}(\overrightarrow{\mathbf{h}})\) and \(\mathbf{P}(\overrightarrow{\mathbf{p}})\) are centroid, orthocentere and circumcentere of a triangle and \(\overrightarrow{\mathbf{x}}+\mathbf{y} \overrightarrow{\mathbf{h}}+\mathbf{z} \mathbf{g}=\mathbf{0}\), then \((x, y, z)=\)

87675 If \(P\) is orthocenter, \(Q\) is circumcentre and \(G\) is centroid of \(\triangle \mathrm{ABC}\), then \(\overline{\mathrm{QP}}=\)

87671 If \(P(1,2,3), R(4,5,-1)\) are the vertices and \(G(2,3,-1)\) is the centroid of \(\triangle P Q R\), then coordinates of midpoint of \(P Q\) are

87672 If \(A, B, C\) and \(D\) are \((3,7,4),(5,-2,3),(-4,5,6)\) and \((1,2,3)\) respectively, then the volume of the parallelopiped with \(A B, A C\) and \(A D\) as the coterminus edges, is (in cubic units)

87673 If \(\mathbf{G}(3,-5, r)\) is centroid of triangle \(A B C\) where \(A(7,-8,1), B(p, q, 5)\) and \(C(q+1,5 p, 0)\) are vertices of a triangle then values of \(p, q, r\) are respectively

87674 If \(\mathbf{G}(\overrightarrow{\mathbf{g}}), \mathbf{H}(\overrightarrow{\mathbf{h}})\) and \(\mathbf{P}(\overrightarrow{\mathbf{p}})\) are centroid, orthocentere and circumcentere of a triangle and \(\overrightarrow{\mathbf{x}}+\mathbf{y} \overrightarrow{\mathbf{h}}+\mathbf{z} \mathbf{g}=\mathbf{0}\), then \((x, y, z)=\)

87675 If \(P\) is orthocenter, \(Q\) is circumcentre and \(G\) is centroid of \(\triangle \mathrm{ABC}\), then \(\overline{\mathrm{QP}}=\)

87671 If \(P(1,2,3), R(4,5,-1)\) are the vertices and \(G(2,3,-1)\) is the centroid of \(\triangle P Q R\), then coordinates of midpoint of \(P Q\) are

87672 If \(A, B, C\) and \(D\) are \((3,7,4),(5,-2,3),(-4,5,6)\) and \((1,2,3)\) respectively, then the volume of the parallelopiped with \(A B, A C\) and \(A D\) as the coterminus edges, is (in cubic units)

87673 If \(\mathbf{G}(3,-5, r)\) is centroid of triangle \(A B C\) where \(A(7,-8,1), B(p, q, 5)\) and \(C(q+1,5 p, 0)\) are vertices of a triangle then values of \(p, q, r\) are respectively

87674 If \(\mathbf{G}(\overrightarrow{\mathbf{g}}), \mathbf{H}(\overrightarrow{\mathbf{h}})\) and \(\mathbf{P}(\overrightarrow{\mathbf{p}})\) are centroid, orthocentere and circumcentere of a triangle and \(\overrightarrow{\mathbf{x}}+\mathbf{y} \overrightarrow{\mathbf{h}}+\mathbf{z} \mathbf{g}=\mathbf{0}\), then \((x, y, z)=\)

87675 If \(P\) is orthocenter, \(Q\) is circumcentre and \(G\) is centroid of \(\triangle \mathrm{ABC}\), then \(\overline{\mathrm{QP}}=\)

87671 If \(P(1,2,3), R(4,5,-1)\) are the vertices and \(G(2,3,-1)\) is the centroid of \(\triangle P Q R\), then coordinates of midpoint of \(P Q\) are

87672 If \(A, B, C\) and \(D\) are \((3,7,4),(5,-2,3),(-4,5,6)\) and \((1,2,3)\) respectively, then the volume of the parallelopiped with \(A B, A C\) and \(A D\) as the coterminus edges, is (in cubic units)

87673 If \(\mathbf{G}(3,-5, r)\) is centroid of triangle \(A B C\) where \(A(7,-8,1), B(p, q, 5)\) and \(C(q+1,5 p, 0)\) are vertices of a triangle then values of \(p, q, r\) are respectively

87674 If \(\mathbf{G}(\overrightarrow{\mathbf{g}}), \mathbf{H}(\overrightarrow{\mathbf{h}})\) and \(\mathbf{P}(\overrightarrow{\mathbf{p}})\) are centroid, orthocentere and circumcentere of a triangle and \(\overrightarrow{\mathbf{x}}+\mathbf{y} \overrightarrow{\mathbf{h}}+\mathbf{z} \mathbf{g}=\mathbf{0}\), then \((x, y, z)=\)

87675 If \(P\) is orthocenter, \(Q\) is circumcentre and \(G\) is centroid of \(\triangle \mathrm{ABC}\), then \(\overline{\mathrm{QP}}=\)

87671 If \(P(1,2,3), R(4,5,-1)\) are the vertices and \(G(2,3,-1)\) is the centroid of \(\triangle P Q R\), then coordinates of midpoint of \(P Q\) are

87672 If \(A, B, C\) and \(D\) are \((3,7,4),(5,-2,3),(-4,5,6)\) and \((1,2,3)\) respectively, then the volume of the parallelopiped with \(A B, A C\) and \(A D\) as the coterminus edges, is (in cubic units)

87673 If \(\mathbf{G}(3,-5, r)\) is centroid of triangle \(A B C\) where \(A(7,-8,1), B(p, q, 5)\) and \(C(q+1,5 p, 0)\) are vertices of a triangle then values of \(p, q, r\) are respectively

87674 If \(\mathbf{G}(\overrightarrow{\mathbf{g}}), \mathbf{H}(\overrightarrow{\mathbf{h}})\) and \(\mathbf{P}(\overrightarrow{\mathbf{p}})\) are centroid, orthocentere and circumcentere of a triangle and \(\overrightarrow{\mathbf{x}}+\mathbf{y} \overrightarrow{\mathbf{h}}+\mathbf{z} \mathbf{g}=\mathbf{0}\), then \((x, y, z)=\)

87675 If \(P\) is orthocenter, \(Q\) is circumcentre and \(G\) is centroid of \(\triangle \mathrm{ABC}\), then \(\overline{\mathrm{QP}}=\)