87878 If \(a, b, c\) are vectors of equal magnitude such that \((a, b)=\alpha,(b, c)=\beta,(c, a)=\gamma\), then the minimum value of \(\cos \alpha+\cos \beta+\cos \gamma\) is

87879 Let ' \(O\) ' be the origin and ' \(\mathrm{P}\) ' be a point which is at a distance of 3 units from the origin. If the direction ratios of \(\overline{\mathrm{OP}}\) are \((1,-2,-2)\) then the coordinates of ' \(P\) ' are

87881 If \(l_1, \mathbf{m}_1, \mathbf{n}_1\) and \(l_2, \mathbf{m}_2, \mathbf{n}_2\) are direction cosines of \(\overline{\mathrm{OA}}\) and \(\overline{\mathrm{OB}}\) such that \(\angle \mathrm{AOB}=\theta\), where \(O\) is the origin, then the direction cosines of the internal angular bisector of \(\angle \mathrm{AOB}\) are

87882 If \(\bar{a}=\bar{i}+2 \bar{j}+3 \bar{k}, \bar{b}=-\bar{i}+2 \bar{j}+\bar{k}, \bar{c}=\bar{i}+2 \bar{j}-2 \bar{k}, n\) is perpendicular to both \(a\) and \(b\) and \(\theta\) is angle between \(\mathrm{c}\) and \(\mathrm{n}\) then \(\sin \theta=\)

87878 If \(a, b, c\) are vectors of equal magnitude such that \((a, b)=\alpha,(b, c)=\beta,(c, a)=\gamma\), then the minimum value of \(\cos \alpha+\cos \beta+\cos \gamma\) is

87879 Let ' \(O\) ' be the origin and ' \(\mathrm{P}\) ' be a point which is at a distance of 3 units from the origin. If the direction ratios of \(\overline{\mathrm{OP}}\) are \((1,-2,-2)\) then the coordinates of ' \(P\) ' are

87881 If \(l_1, \mathbf{m}_1, \mathbf{n}_1\) and \(l_2, \mathbf{m}_2, \mathbf{n}_2\) are direction cosines of \(\overline{\mathrm{OA}}\) and \(\overline{\mathrm{OB}}\) such that \(\angle \mathrm{AOB}=\theta\), where \(O\) is the origin, then the direction cosines of the internal angular bisector of \(\angle \mathrm{AOB}\) are

87882 If \(\bar{a}=\bar{i}+2 \bar{j}+3 \bar{k}, \bar{b}=-\bar{i}+2 \bar{j}+\bar{k}, \bar{c}=\bar{i}+2 \bar{j}-2 \bar{k}, n\) is perpendicular to both \(a\) and \(b\) and \(\theta\) is angle between \(\mathrm{c}\) and \(\mathrm{n}\) then \(\sin \theta=\)

87878 If \(a, b, c\) are vectors of equal magnitude such that \((a, b)=\alpha,(b, c)=\beta,(c, a)=\gamma\), then the minimum value of \(\cos \alpha+\cos \beta+\cos \gamma\) is

87879 Let ' \(O\) ' be the origin and ' \(\mathrm{P}\) ' be a point which is at a distance of 3 units from the origin. If the direction ratios of \(\overline{\mathrm{OP}}\) are \((1,-2,-2)\) then the coordinates of ' \(P\) ' are

87881 If \(l_1, \mathbf{m}_1, \mathbf{n}_1\) and \(l_2, \mathbf{m}_2, \mathbf{n}_2\) are direction cosines of \(\overline{\mathrm{OA}}\) and \(\overline{\mathrm{OB}}\) such that \(\angle \mathrm{AOB}=\theta\), where \(O\) is the origin, then the direction cosines of the internal angular bisector of \(\angle \mathrm{AOB}\) are

87882 If \(\bar{a}=\bar{i}+2 \bar{j}+3 \bar{k}, \bar{b}=-\bar{i}+2 \bar{j}+\bar{k}, \bar{c}=\bar{i}+2 \bar{j}-2 \bar{k}, n\) is perpendicular to both \(a\) and \(b\) and \(\theta\) is angle between \(\mathrm{c}\) and \(\mathrm{n}\) then \(\sin \theta=\)

87878 If \(a, b, c\) are vectors of equal magnitude such that \((a, b)=\alpha,(b, c)=\beta,(c, a)=\gamma\), then the minimum value of \(\cos \alpha+\cos \beta+\cos \gamma\) is

87879 Let ' \(O\) ' be the origin and ' \(\mathrm{P}\) ' be a point which is at a distance of 3 units from the origin. If the direction ratios of \(\overline{\mathrm{OP}}\) are \((1,-2,-2)\) then the coordinates of ' \(P\) ' are

87881 If \(l_1, \mathbf{m}_1, \mathbf{n}_1\) and \(l_2, \mathbf{m}_2, \mathbf{n}_2\) are direction cosines of \(\overline{\mathrm{OA}}\) and \(\overline{\mathrm{OB}}\) such that \(\angle \mathrm{AOB}=\theta\), where \(O\) is the origin, then the direction cosines of the internal angular bisector of \(\angle \mathrm{AOB}\) are

87882 If \(\bar{a}=\bar{i}+2 \bar{j}+3 \bar{k}, \bar{b}=-\bar{i}+2 \bar{j}+\bar{k}, \bar{c}=\bar{i}+2 \bar{j}-2 \bar{k}, n\) is perpendicular to both \(a\) and \(b\) and \(\theta\) is angle between \(\mathrm{c}\) and \(\mathrm{n}\) then \(\sin \theta=\)