87716 The projection of a line segment \(O P\) through origin \(O\), on the coordinate axes are \(8,5,6\). Then the length of the line segment \(O P\) is equal to

87717 The ratio in which \(\mathrm{ZX}\)-plane divides the line segment \(A B\) joining the points \(A(4,2,3)\) and \(B\) \((-2,4,5)\) is equal to

87718 If \(\vec{a}, \vec{b}, \vec{c}\) are the three unit vectors such that \(|\vec{a}+\vec{b}+\vec{c}|=1\) and \(\vec{b}\) is perpendicular to \(\vec{c}\), if \(\vec{a}\) makes angles \(\alpha, \beta\) with \(\vec{b}\) and \(\vec{c}\) respectively, then \(\cos \alpha+\cos \beta\) has the value

87719 The position vector of a point that divides the line segment joining \(P=(1,2,-1)\) and \(Q=(-1\), 1,1 ) externally in the ratio \(1: 2: 3\), is

87716 The projection of a line segment \(O P\) through origin \(O\), on the coordinate axes are \(8,5,6\). Then the length of the line segment \(O P\) is equal to

87717 The ratio in which \(\mathrm{ZX}\)-plane divides the line segment \(A B\) joining the points \(A(4,2,3)\) and \(B\) \((-2,4,5)\) is equal to

87718 If \(\vec{a}, \vec{b}, \vec{c}\) are the three unit vectors such that \(|\vec{a}+\vec{b}+\vec{c}|=1\) and \(\vec{b}\) is perpendicular to \(\vec{c}\), if \(\vec{a}\) makes angles \(\alpha, \beta\) with \(\vec{b}\) and \(\vec{c}\) respectively, then \(\cos \alpha+\cos \beta\) has the value

87719 The position vector of a point that divides the line segment joining \(P=(1,2,-1)\) and \(Q=(-1\), 1,1 ) externally in the ratio \(1: 2: 3\), is

87716 The projection of a line segment \(O P\) through origin \(O\), on the coordinate axes are \(8,5,6\). Then the length of the line segment \(O P\) is equal to

87717 The ratio in which \(\mathrm{ZX}\)-plane divides the line segment \(A B\) joining the points \(A(4,2,3)\) and \(B\) \((-2,4,5)\) is equal to

87718 If \(\vec{a}, \vec{b}, \vec{c}\) are the three unit vectors such that \(|\vec{a}+\vec{b}+\vec{c}|=1\) and \(\vec{b}\) is perpendicular to \(\vec{c}\), if \(\vec{a}\) makes angles \(\alpha, \beta\) with \(\vec{b}\) and \(\vec{c}\) respectively, then \(\cos \alpha+\cos \beta\) has the value

87719 The position vector of a point that divides the line segment joining \(P=(1,2,-1)\) and \(Q=(-1\), 1,1 ) externally in the ratio \(1: 2: 3\), is

87716 The projection of a line segment \(O P\) through origin \(O\), on the coordinate axes are \(8,5,6\). Then the length of the line segment \(O P\) is equal to

87717 The ratio in which \(\mathrm{ZX}\)-plane divides the line segment \(A B\) joining the points \(A(4,2,3)\) and \(B\) \((-2,4,5)\) is equal to

87718 If \(\vec{a}, \vec{b}, \vec{c}\) are the three unit vectors such that \(|\vec{a}+\vec{b}+\vec{c}|=1\) and \(\vec{b}\) is perpendicular to \(\vec{c}\), if \(\vec{a}\) makes angles \(\alpha, \beta\) with \(\vec{b}\) and \(\vec{c}\) respectively, then \(\cos \alpha+\cos \beta\) has the value

87719 The position vector of a point that divides the line segment joining \(P=(1,2,-1)\) and \(Q=(-1\), 1,1 ) externally in the ratio \(1: 2: 3\), is