87798 Let \(x \in R\) and \(\log _2 x>0\). Then the vectors \(\vec{A}=\) (2, \(\left.\log _2 x, s\right) . \vec{B}=\left(\log _2 x, s, \log _2 x\right)\) include an acute angle if

87799 Let ABCDEF be a regular hexagon with the vertices \(A, B, C, D, E, F\) counterclockwise. Then the vector \(\overrightarrow{A B}+\overrightarrow{B C}\) is equal/parallel to

87800 If \(\triangle O \mathrm{AC}\), if \(\mathrm{B}\) is the midpoint of side \(\mathrm{AC}\) and \(\overrightarrow{\mathrm{OA}}=\overrightarrow{\mathbf{a}}, \overrightarrow{\mathrm{OB}}=\overrightarrow{\mathbf{b}}\) then \(\overrightarrow{\mathrm{OC}}=\)

87801 Let \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}\) be a vector such that \(\vec{a} \times \vec{c}+\vec{b}=0\) and \(\vec{a} . \vec{c}=4\), then \(|\vec{c}|^2\) is equal to

87802 Let \(\alpha \in R\) and three vectors \(\vec{a}=\alpha \hat{i}+\hat{j}+3 \hat{k}\), \(\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\alpha \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{c}}=\alpha \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\). Then, the set \(S=(\boldsymbol{\alpha}: \mathbf{a}, \mathbf{b}\) and \(\mathrm{c}\) are coplanar)

87798 Let \(x \in R\) and \(\log _2 x>0\). Then the vectors \(\vec{A}=\) (2, \(\left.\log _2 x, s\right) . \vec{B}=\left(\log _2 x, s, \log _2 x\right)\) include an acute angle if

87799 Let ABCDEF be a regular hexagon with the vertices \(A, B, C, D, E, F\) counterclockwise. Then the vector \(\overrightarrow{A B}+\overrightarrow{B C}\) is equal/parallel to

87800 If \(\triangle O \mathrm{AC}\), if \(\mathrm{B}\) is the midpoint of side \(\mathrm{AC}\) and \(\overrightarrow{\mathrm{OA}}=\overrightarrow{\mathbf{a}}, \overrightarrow{\mathrm{OB}}=\overrightarrow{\mathbf{b}}\) then \(\overrightarrow{\mathrm{OC}}=\)

87801 Let \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}\) be a vector such that \(\vec{a} \times \vec{c}+\vec{b}=0\) and \(\vec{a} . \vec{c}=4\), then \(|\vec{c}|^2\) is equal to

87802 Let \(\alpha \in R\) and three vectors \(\vec{a}=\alpha \hat{i}+\hat{j}+3 \hat{k}\), \(\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\alpha \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{c}}=\alpha \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\). Then, the set \(S=(\boldsymbol{\alpha}: \mathbf{a}, \mathbf{b}\) and \(\mathrm{c}\) are coplanar)

87798 Let \(x \in R\) and \(\log _2 x>0\). Then the vectors \(\vec{A}=\) (2, \(\left.\log _2 x, s\right) . \vec{B}=\left(\log _2 x, s, \log _2 x\right)\) include an acute angle if

87799 Let ABCDEF be a regular hexagon with the vertices \(A, B, C, D, E, F\) counterclockwise. Then the vector \(\overrightarrow{A B}+\overrightarrow{B C}\) is equal/parallel to

87800 If \(\triangle O \mathrm{AC}\), if \(\mathrm{B}\) is the midpoint of side \(\mathrm{AC}\) and \(\overrightarrow{\mathrm{OA}}=\overrightarrow{\mathbf{a}}, \overrightarrow{\mathrm{OB}}=\overrightarrow{\mathbf{b}}\) then \(\overrightarrow{\mathrm{OC}}=\)

87801 Let \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}\) be a vector such that \(\vec{a} \times \vec{c}+\vec{b}=0\) and \(\vec{a} . \vec{c}=4\), then \(|\vec{c}|^2\) is equal to

87802 Let \(\alpha \in R\) and three vectors \(\vec{a}=\alpha \hat{i}+\hat{j}+3 \hat{k}\), \(\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\alpha \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{c}}=\alpha \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\). Then, the set \(S=(\boldsymbol{\alpha}: \mathbf{a}, \mathbf{b}\) and \(\mathrm{c}\) are coplanar)

87798 Let \(x \in R\) and \(\log _2 x>0\). Then the vectors \(\vec{A}=\) (2, \(\left.\log _2 x, s\right) . \vec{B}=\left(\log _2 x, s, \log _2 x\right)\) include an acute angle if

87799 Let ABCDEF be a regular hexagon with the vertices \(A, B, C, D, E, F\) counterclockwise. Then the vector \(\overrightarrow{A B}+\overrightarrow{B C}\) is equal/parallel to

87800 If \(\triangle O \mathrm{AC}\), if \(\mathrm{B}\) is the midpoint of side \(\mathrm{AC}\) and \(\overrightarrow{\mathrm{OA}}=\overrightarrow{\mathbf{a}}, \overrightarrow{\mathrm{OB}}=\overrightarrow{\mathbf{b}}\) then \(\overrightarrow{\mathrm{OC}}=\)

87801 Let \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}\) be a vector such that \(\vec{a} \times \vec{c}+\vec{b}=0\) and \(\vec{a} . \vec{c}=4\), then \(|\vec{c}|^2\) is equal to

87802 Let \(\alpha \in R\) and three vectors \(\vec{a}=\alpha \hat{i}+\hat{j}+3 \hat{k}\), \(\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\alpha \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{c}}=\alpha \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\). Then, the set \(S=(\boldsymbol{\alpha}: \mathbf{a}, \mathbf{b}\) and \(\mathrm{c}\) are coplanar)

87798 Let \(x \in R\) and \(\log _2 x>0\). Then the vectors \(\vec{A}=\) (2, \(\left.\log _2 x, s\right) . \vec{B}=\left(\log _2 x, s, \log _2 x\right)\) include an acute angle if

87799 Let ABCDEF be a regular hexagon with the vertices \(A, B, C, D, E, F\) counterclockwise. Then the vector \(\overrightarrow{A B}+\overrightarrow{B C}\) is equal/parallel to

87800 If \(\triangle O \mathrm{AC}\), if \(\mathrm{B}\) is the midpoint of side \(\mathrm{AC}\) and \(\overrightarrow{\mathrm{OA}}=\overrightarrow{\mathbf{a}}, \overrightarrow{\mathrm{OB}}=\overrightarrow{\mathbf{b}}\) then \(\overrightarrow{\mathrm{OC}}=\)

87801 Let \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \overrightarrow{\mathbf{b}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}\) be a vector such that \(\vec{a} \times \vec{c}+\vec{b}=0\) and \(\vec{a} . \vec{c}=4\), then \(|\vec{c}|^2\) is equal to

87802 Let \(\alpha \in R\) and three vectors \(\vec{a}=\alpha \hat{i}+\hat{j}+3 \hat{k}\), \(\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\alpha \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{c}}=\alpha \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\). Then, the set \(S=(\boldsymbol{\alpha}: \mathbf{a}, \mathbf{b}\) and \(\mathrm{c}\) are coplanar)