Distance, Position and Section Formula of Vector
Vector Algebra

87663 The perimeter of the triangle whose vertices have the position vectors \(\hat{i}+\hat{j}+\hat{k}, 5 \hat{i}+3 \hat{j}-3 \hat{k}\) and \(2 \hat{i}+5 \hat{j}+9 \hat{k}\) is

1 \((\sqrt{15}-\sqrt{157})\) units
2 \((\sqrt{15}+\sqrt{157})\) units
3 \((15-\sqrt{157})\) units
4 \((15+\sqrt{157})\) units
Vector Algebra

87664 If the origin is the centroid of the triangle whose vertices are \(A(2, p,-3), B(q,-2,5)\) and \(C(-5,1, r)\) then

1 \(\mathrm{p}=1, \mathrm{q}=3, \mathrm{r}=2\)
2 \(\mathrm{p}=1, \mathrm{q}=3, \mathrm{r}=-2\)
3 \(\mathrm{p}=1, \mathrm{q}=-3, \mathrm{r}=-2\)
4 \(\mathrm{p}=-1, \mathrm{q}=3, \mathrm{r}=-2\)
Vector Algebra

87665 If \(A(0,4,0), B(0,0,3)\) and \(C(0,4,3)\) are the vertices of \(\triangle \mathrm{ABC}\), then its incentre is,

1 \((0,3,2)\)
2 \((3,0,2)\)
3 \((0,2,3)\)
4 \((2,0,3)\)
Vector Algebra

87666 If \(a, b, c\) are lengths of the sides \(\mathbf{B C}, \mathbf{C A}, \mathbf{A B}\) respectively of \(\triangle A B C\) and \(H\) is any point in the plane of \(\triangle \mathrm{ABC}\) such that \(\mathrm{a}\) \(\mathbf{a A \vec { H }}+b \overrightarrow{B H}+c \overrightarrow{C H}=\overrightarrow{0}\), then \(H\) is the

1 Incetnre of \(\triangle A B C\)
2 Orthocentre of \(\triangle \mathrm{ABC}\)
3 Circumcentre of \(\triangle \mathrm{ABC}\)
4 Centroid of \(\triangle \mathrm{ABC}\)
Vector Algebra

87663 The perimeter of the triangle whose vertices have the position vectors \(\hat{i}+\hat{j}+\hat{k}, 5 \hat{i}+3 \hat{j}-3 \hat{k}\) and \(2 \hat{i}+5 \hat{j}+9 \hat{k}\) is

1 \((\sqrt{15}-\sqrt{157})\) units
2 \((\sqrt{15}+\sqrt{157})\) units
3 \((15-\sqrt{157})\) units
4 \((15+\sqrt{157})\) units
Vector Algebra

87664 If the origin is the centroid of the triangle whose vertices are \(A(2, p,-3), B(q,-2,5)\) and \(C(-5,1, r)\) then

1 \(\mathrm{p}=1, \mathrm{q}=3, \mathrm{r}=2\)
2 \(\mathrm{p}=1, \mathrm{q}=3, \mathrm{r}=-2\)
3 \(\mathrm{p}=1, \mathrm{q}=-3, \mathrm{r}=-2\)
4 \(\mathrm{p}=-1, \mathrm{q}=3, \mathrm{r}=-2\)
Vector Algebra

87665 If \(A(0,4,0), B(0,0,3)\) and \(C(0,4,3)\) are the vertices of \(\triangle \mathrm{ABC}\), then its incentre is,

1 \((0,3,2)\)
2 \((3,0,2)\)
3 \((0,2,3)\)
4 \((2,0,3)\)
Vector Algebra

87666 If \(a, b, c\) are lengths of the sides \(\mathbf{B C}, \mathbf{C A}, \mathbf{A B}\) respectively of \(\triangle A B C\) and \(H\) is any point in the plane of \(\triangle \mathrm{ABC}\) such that \(\mathrm{a}\) \(\mathbf{a A \vec { H }}+b \overrightarrow{B H}+c \overrightarrow{C H}=\overrightarrow{0}\), then \(H\) is the

1 Incetnre of \(\triangle A B C\)
2 Orthocentre of \(\triangle \mathrm{ABC}\)
3 Circumcentre of \(\triangle \mathrm{ABC}\)
4 Centroid of \(\triangle \mathrm{ABC}\)
Vector Algebra

87663 The perimeter of the triangle whose vertices have the position vectors \(\hat{i}+\hat{j}+\hat{k}, 5 \hat{i}+3 \hat{j}-3 \hat{k}\) and \(2 \hat{i}+5 \hat{j}+9 \hat{k}\) is

1 \((\sqrt{15}-\sqrt{157})\) units
2 \((\sqrt{15}+\sqrt{157})\) units
3 \((15-\sqrt{157})\) units
4 \((15+\sqrt{157})\) units
Vector Algebra

87664 If the origin is the centroid of the triangle whose vertices are \(A(2, p,-3), B(q,-2,5)\) and \(C(-5,1, r)\) then

1 \(\mathrm{p}=1, \mathrm{q}=3, \mathrm{r}=2\)
2 \(\mathrm{p}=1, \mathrm{q}=3, \mathrm{r}=-2\)
3 \(\mathrm{p}=1, \mathrm{q}=-3, \mathrm{r}=-2\)
4 \(\mathrm{p}=-1, \mathrm{q}=3, \mathrm{r}=-2\)
Vector Algebra

87665 If \(A(0,4,0), B(0,0,3)\) and \(C(0,4,3)\) are the vertices of \(\triangle \mathrm{ABC}\), then its incentre is,

1 \((0,3,2)\)
2 \((3,0,2)\)
3 \((0,2,3)\)
4 \((2,0,3)\)
Vector Algebra

87666 If \(a, b, c\) are lengths of the sides \(\mathbf{B C}, \mathbf{C A}, \mathbf{A B}\) respectively of \(\triangle A B C\) and \(H\) is any point in the plane of \(\triangle \mathrm{ABC}\) such that \(\mathrm{a}\) \(\mathbf{a A \vec { H }}+b \overrightarrow{B H}+c \overrightarrow{C H}=\overrightarrow{0}\), then \(H\) is the

1 Incetnre of \(\triangle A B C\)
2 Orthocentre of \(\triangle \mathrm{ABC}\)
3 Circumcentre of \(\triangle \mathrm{ABC}\)
4 Centroid of \(\triangle \mathrm{ABC}\)
Vector Algebra

87663 The perimeter of the triangle whose vertices have the position vectors \(\hat{i}+\hat{j}+\hat{k}, 5 \hat{i}+3 \hat{j}-3 \hat{k}\) and \(2 \hat{i}+5 \hat{j}+9 \hat{k}\) is

1 \((\sqrt{15}-\sqrt{157})\) units
2 \((\sqrt{15}+\sqrt{157})\) units
3 \((15-\sqrt{157})\) units
4 \((15+\sqrt{157})\) units
Vector Algebra

87664 If the origin is the centroid of the triangle whose vertices are \(A(2, p,-3), B(q,-2,5)\) and \(C(-5,1, r)\) then

1 \(\mathrm{p}=1, \mathrm{q}=3, \mathrm{r}=2\)
2 \(\mathrm{p}=1, \mathrm{q}=3, \mathrm{r}=-2\)
3 \(\mathrm{p}=1, \mathrm{q}=-3, \mathrm{r}=-2\)
4 \(\mathrm{p}=-1, \mathrm{q}=3, \mathrm{r}=-2\)
Vector Algebra

87665 If \(A(0,4,0), B(0,0,3)\) and \(C(0,4,3)\) are the vertices of \(\triangle \mathrm{ABC}\), then its incentre is,

1 \((0,3,2)\)
2 \((3,0,2)\)
3 \((0,2,3)\)
4 \((2,0,3)\)
Vector Algebra

87666 If \(a, b, c\) are lengths of the sides \(\mathbf{B C}, \mathbf{C A}, \mathbf{A B}\) respectively of \(\triangle A B C\) and \(H\) is any point in the plane of \(\triangle \mathrm{ABC}\) such that \(\mathrm{a}\) \(\mathbf{a A \vec { H }}+b \overrightarrow{B H}+c \overrightarrow{C H}=\overrightarrow{0}\), then \(H\) is the

1 Incetnre of \(\triangle A B C\)
2 Orthocentre of \(\triangle \mathrm{ABC}\)
3 Circumcentre of \(\triangle \mathrm{ABC}\)
4 Centroid of \(\triangle \mathrm{ABC}\)