88006 The volume of the tetrahedron whose coterminous edges are \(\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}\) is

88007 If \(\overrightarrow{\mathrm{u}}_1\) and \(\overrightarrow{\mathrm{u}}_2\) be vectors of unit length and \(\theta\) be the angle between them, then \(\frac{1}{2}\left|\overrightarrow{\mathbf{u}}_2-\overrightarrow{\mathbf{u}}_1\right|\) is

88008 If \(\overrightarrow{\mathbf{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=\overrightarrow{\mathbf{0}}\) and \(|\overrightarrow{\mathrm{a}}|=7,|\overrightarrow{\mathrm{b}}|=3,|\overrightarrow{\mathrm{c}}|=5\) then angle between \(\overrightarrow{\mathbf{b}}\) and \(\overrightarrow{\mathbf{c}}\) is

88009 A particle is acted on by a force of 6 units in the direction \(9 \hat{i}+6 \hat{j}+2 \hat{k}\) and is displaced from the point \(3 \hat{i}+4 \hat{j}-15 \hat{k}\) to the point \(7 \hat{i}-6 \hat{j}+8 \hat{k}\). The work done is

88006 The volume of the tetrahedron whose coterminous edges are \(\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}\) is

88007 If \(\overrightarrow{\mathrm{u}}_1\) and \(\overrightarrow{\mathrm{u}}_2\) be vectors of unit length and \(\theta\) be the angle between them, then \(\frac{1}{2}\left|\overrightarrow{\mathbf{u}}_2-\overrightarrow{\mathbf{u}}_1\right|\) is

88008 If \(\overrightarrow{\mathbf{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=\overrightarrow{\mathbf{0}}\) and \(|\overrightarrow{\mathrm{a}}|=7,|\overrightarrow{\mathrm{b}}|=3,|\overrightarrow{\mathrm{c}}|=5\) then angle between \(\overrightarrow{\mathbf{b}}\) and \(\overrightarrow{\mathbf{c}}\) is

88009 A particle is acted on by a force of 6 units in the direction \(9 \hat{i}+6 \hat{j}+2 \hat{k}\) and is displaced from the point \(3 \hat{i}+4 \hat{j}-15 \hat{k}\) to the point \(7 \hat{i}-6 \hat{j}+8 \hat{k}\). The work done is

88006 The volume of the tetrahedron whose coterminous edges are \(\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}\) is

88007 If \(\overrightarrow{\mathrm{u}}_1\) and \(\overrightarrow{\mathrm{u}}_2\) be vectors of unit length and \(\theta\) be the angle between them, then \(\frac{1}{2}\left|\overrightarrow{\mathbf{u}}_2-\overrightarrow{\mathbf{u}}_1\right|\) is

88008 If \(\overrightarrow{\mathbf{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=\overrightarrow{\mathbf{0}}\) and \(|\overrightarrow{\mathrm{a}}|=7,|\overrightarrow{\mathrm{b}}|=3,|\overrightarrow{\mathrm{c}}|=5\) then angle between \(\overrightarrow{\mathbf{b}}\) and \(\overrightarrow{\mathbf{c}}\) is

88009 A particle is acted on by a force of 6 units in the direction \(9 \hat{i}+6 \hat{j}+2 \hat{k}\) and is displaced from the point \(3 \hat{i}+4 \hat{j}-15 \hat{k}\) to the point \(7 \hat{i}-6 \hat{j}+8 \hat{k}\). The work done is

88006 The volume of the tetrahedron whose coterminous edges are \(\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}\) is

88007 If \(\overrightarrow{\mathrm{u}}_1\) and \(\overrightarrow{\mathrm{u}}_2\) be vectors of unit length and \(\theta\) be the angle between them, then \(\frac{1}{2}\left|\overrightarrow{\mathbf{u}}_2-\overrightarrow{\mathbf{u}}_1\right|\) is

88008 If \(\overrightarrow{\mathbf{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=\overrightarrow{\mathbf{0}}\) and \(|\overrightarrow{\mathrm{a}}|=7,|\overrightarrow{\mathrm{b}}|=3,|\overrightarrow{\mathrm{c}}|=5\) then angle between \(\overrightarrow{\mathbf{b}}\) and \(\overrightarrow{\mathbf{c}}\) is

88009 A particle is acted on by a force of 6 units in the direction \(9 \hat{i}+6 \hat{j}+2 \hat{k}\) and is displaced from the point \(3 \hat{i}+4 \hat{j}-15 \hat{k}\) to the point \(7 \hat{i}-6 \hat{j}+8 \hat{k}\). The work done is