87776 Let collinear points \(A, B\) and \(C\) be such that \(\overrightarrow{\mathrm{BC}}=2 \overrightarrow{\mathrm{AB}}\). Then \(\mathrm{AC}: \mathrm{CB}\) is

87777 Consider the points \(P(3,4,-3)\) and \(Q(-1,9,0)\). If a vector \(\overrightarrow{\mathbf{u}}\) is represented by the directed line segment \(\overline{\mathbf{P Q}}\) then the point \(R\) such that \(\overrightarrow{\mathrm{QP}}\) also represents \(\overrightarrow{\mathbf{u}}\) is

87778 \(A B C\) is a right-angled triangle in which \(\max\) \(\{A B, B C, A C\}=B C\). If the position vectors of \(B\) and \(C\) are respectively \(3 \hat{i}-2 \hat{j}+\hat{k}\) and \(5 \hat{i}+\) \(\hat{\mathbf{j}}-3 \hat{\mathbf{k}}\), then
\(\overrightarrow{\mathbf{A B}} \cdot \overrightarrow{\mathbf{A C}}+\overrightarrow{\mathbf{B A}} \cdot \overrightarrow{\mathbf{B C}}+\overrightarrow{\mathbf{C A}} \cdot \overrightarrow{\mathbf{C B}}=\)

87779 If \(\vec{a}, \vec{b}\) are two unit vectors inclined at angle \(\theta\) such that \(\vec{a}+\vec{b}\) is a unit vector, then what is \(\theta\) equal to?

87776 Let collinear points \(A, B\) and \(C\) be such that \(\overrightarrow{\mathrm{BC}}=2 \overrightarrow{\mathrm{AB}}\). Then \(\mathrm{AC}: \mathrm{CB}\) is

87777 Consider the points \(P(3,4,-3)\) and \(Q(-1,9,0)\). If a vector \(\overrightarrow{\mathbf{u}}\) is represented by the directed line segment \(\overline{\mathbf{P Q}}\) then the point \(R\) such that \(\overrightarrow{\mathrm{QP}}\) also represents \(\overrightarrow{\mathbf{u}}\) is

87778 \(A B C\) is a right-angled triangle in which \(\max\) \(\{A B, B C, A C\}=B C\). If the position vectors of \(B\) and \(C\) are respectively \(3 \hat{i}-2 \hat{j}+\hat{k}\) and \(5 \hat{i}+\) \(\hat{\mathbf{j}}-3 \hat{\mathbf{k}}\), then
\(\overrightarrow{\mathbf{A B}} \cdot \overrightarrow{\mathbf{A C}}+\overrightarrow{\mathbf{B A}} \cdot \overrightarrow{\mathbf{B C}}+\overrightarrow{\mathbf{C A}} \cdot \overrightarrow{\mathbf{C B}}=\)

87779 If \(\vec{a}, \vec{b}\) are two unit vectors inclined at angle \(\theta\) such that \(\vec{a}+\vec{b}\) is a unit vector, then what is \(\theta\) equal to?

87776 Let collinear points \(A, B\) and \(C\) be such that \(\overrightarrow{\mathrm{BC}}=2 \overrightarrow{\mathrm{AB}}\). Then \(\mathrm{AC}: \mathrm{CB}\) is

87777 Consider the points \(P(3,4,-3)\) and \(Q(-1,9,0)\). If a vector \(\overrightarrow{\mathbf{u}}\) is represented by the directed line segment \(\overline{\mathbf{P Q}}\) then the point \(R\) such that \(\overrightarrow{\mathrm{QP}}\) also represents \(\overrightarrow{\mathbf{u}}\) is

87778 \(A B C\) is a right-angled triangle in which \(\max\) \(\{A B, B C, A C\}=B C\). If the position vectors of \(B\) and \(C\) are respectively \(3 \hat{i}-2 \hat{j}+\hat{k}\) and \(5 \hat{i}+\) \(\hat{\mathbf{j}}-3 \hat{\mathbf{k}}\), then
\(\overrightarrow{\mathbf{A B}} \cdot \overrightarrow{\mathbf{A C}}+\overrightarrow{\mathbf{B A}} \cdot \overrightarrow{\mathbf{B C}}+\overrightarrow{\mathbf{C A}} \cdot \overrightarrow{\mathbf{C B}}=\)

87779 If \(\vec{a}, \vec{b}\) are two unit vectors inclined at angle \(\theta\) such that \(\vec{a}+\vec{b}\) is a unit vector, then what is \(\theta\) equal to?

87776 Let collinear points \(A, B\) and \(C\) be such that \(\overrightarrow{\mathrm{BC}}=2 \overrightarrow{\mathrm{AB}}\). Then \(\mathrm{AC}: \mathrm{CB}\) is

87777 Consider the points \(P(3,4,-3)\) and \(Q(-1,9,0)\). If a vector \(\overrightarrow{\mathbf{u}}\) is represented by the directed line segment \(\overline{\mathbf{P Q}}\) then the point \(R\) such that \(\overrightarrow{\mathrm{QP}}\) also represents \(\overrightarrow{\mathbf{u}}\) is

87778 \(A B C\) is a right-angled triangle in which \(\max\) \(\{A B, B C, A C\}=B C\). If the position vectors of \(B\) and \(C\) are respectively \(3 \hat{i}-2 \hat{j}+\hat{k}\) and \(5 \hat{i}+\) \(\hat{\mathbf{j}}-3 \hat{\mathbf{k}}\), then
\(\overrightarrow{\mathbf{A B}} \cdot \overrightarrow{\mathbf{A C}}+\overrightarrow{\mathbf{B A}} \cdot \overrightarrow{\mathbf{B C}}+\overrightarrow{\mathbf{C A}} \cdot \overrightarrow{\mathbf{C B}}=\)

87779 If \(\vec{a}, \vec{b}\) are two unit vectors inclined at angle \(\theta\) such that \(\vec{a}+\vec{b}\) is a unit vector, then what is \(\theta\) equal to?