87750 If the vectors $\overrightarrow{AB}=-3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a triangle $ABC$. Then the length of the median through $A$ is

87751 If $|\overrightarrow{a}|=2,|\overrightarrow{b}|=3,|\overrightarrow{c}|=4$ and $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$, then the value of $\overrightarrow{\mathbf{b}}\cdot \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}}\cdot \overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{b}}$ is equal to

87752 If the vectors $\overrightarrow{i}+3\overrightarrow{j}-2\overrightarrow{k},2\overrightarrow{i}-\overrightarrow{j}+4\overrightarrow{k}$ and $\mathbf{3}\overrightarrow{\mathbf{i}}+\mathbf{2}\overrightarrow{j}+\mathbf{x}\overrightarrow{k}$ are coplanar, then the value of $x$ is:

87749 If the points with position vectors $-\hat{\mathbf{j}}-\hat{k},4\hat{i}+5\hat{j}+\lambda \hat{k},3\hat{i}+9\hat{j}+4\hat{k}$ and $-4\hat{i}+4\hat{j}+4\hat{k}$ are coplanar, then $\lambda$ equals

87750 If the vectors $\overrightarrow{AB}=-3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a triangle $ABC$. Then the length of the median through $A$ is

87751 If $|\overrightarrow{a}|=2,|\overrightarrow{b}|=3,|\overrightarrow{c}|=4$ and $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$, then the value of $\overrightarrow{\mathbf{b}}\cdot \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}}\cdot \overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{b}}$ is equal to

87752 If the vectors $\overrightarrow{i}+3\overrightarrow{j}-2\overrightarrow{k},2\overrightarrow{i}-\overrightarrow{j}+4\overrightarrow{k}$ and $\mathbf{3}\overrightarrow{\mathbf{i}}+\mathbf{2}\overrightarrow{j}+\mathbf{x}\overrightarrow{k}$ are coplanar, then the value of $x$ is:

87749 If the points with position vectors $-\hat{\mathbf{j}}-\hat{k},4\hat{i}+5\hat{j}+\lambda \hat{k},3\hat{i}+9\hat{j}+4\hat{k}$ and $-4\hat{i}+4\hat{j}+4\hat{k}$ are coplanar, then $\lambda$ equals

87750 If the vectors $\overrightarrow{AB}=-3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a triangle $ABC$. Then the length of the median through $A$ is

87751 If $|\overrightarrow{a}|=2,|\overrightarrow{b}|=3,|\overrightarrow{c}|=4$ and $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$, then the value of $\overrightarrow{\mathbf{b}}\cdot \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}}\cdot \overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{b}}$ is equal to

87752 If the vectors $\overrightarrow{i}+3\overrightarrow{j}-2\overrightarrow{k},2\overrightarrow{i}-\overrightarrow{j}+4\overrightarrow{k}$ and $\mathbf{3}\overrightarrow{\mathbf{i}}+\mathbf{2}\overrightarrow{j}+\mathbf{x}\overrightarrow{k}$ are coplanar, then the value of $x$ is:

87749 If the points with position vectors $-\hat{\mathbf{j}}-\hat{k},4\hat{i}+5\hat{j}+\lambda \hat{k},3\hat{i}+9\hat{j}+4\hat{k}$ and $-4\hat{i}+4\hat{j}+4\hat{k}$ are coplanar, then $\lambda$ equals

87750 If the vectors $\overrightarrow{AB}=-3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a triangle $ABC$. Then the length of the median through $A$ is

87751 If $|\overrightarrow{a}|=2,|\overrightarrow{b}|=3,|\overrightarrow{c}|=4$ and $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$, then the value of $\overrightarrow{\mathbf{b}}\cdot \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}}\cdot \overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{b}}$ is equal to

87752 If the vectors $\overrightarrow{i}+3\overrightarrow{j}-2\overrightarrow{k},2\overrightarrow{i}-\overrightarrow{j}+4\overrightarrow{k}$ and $\mathbf{3}\overrightarrow{\mathbf{i}}+\mathbf{2}\overrightarrow{j}+\mathbf{x}\overrightarrow{k}$ are coplanar, then the value of $x$ is: