121142 If \(\cos \theta=\frac{\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma}{\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma} \alpha, \beta, \gamma \quad\) are the angles made by a line with the positive directions of the axes of reference, then the measure of \(\theta\) is

121143 If \(P(1,2,3)\) is the given point and \(P N\) is the length of perpendicular from \(P\) on the given
line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}\), then \(P N=\)

121144 If the foot of the perpendicular from the point \(A(-1,4,3)\) on the plane \(P: 2 x+m y+n z=4\), is \(\left(-2, \frac{7}{2}, \frac{3}{2}\right)\), then the distance of the point \(A\) from the plane, measured parallel to a line with direction ratio \(3,-1,-4\), is equal to :

121145 A line makes the same angle \(\theta\) with each of \(x\) axis and \(z\)-axis. If it makes an angle \(\beta\) with the \(y\)-axis such that \(\sin ^2 \beta=3 \sin ^2 \theta\), what is \(\cos ^2 \theta\) equal to ?

121142 If \(\cos \theta=\frac{\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma}{\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma} \alpha, \beta, \gamma \quad\) are the angles made by a line with the positive directions of the axes of reference, then the measure of \(\theta\) is

121143 If \(P(1,2,3)\) is the given point and \(P N\) is the length of perpendicular from \(P\) on the given
line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}\), then \(P N=\)

121144 If the foot of the perpendicular from the point \(A(-1,4,3)\) on the plane \(P: 2 x+m y+n z=4\), is \(\left(-2, \frac{7}{2}, \frac{3}{2}\right)\), then the distance of the point \(A\) from the plane, measured parallel to a line with direction ratio \(3,-1,-4\), is equal to :

121145 A line makes the same angle \(\theta\) with each of \(x\) axis and \(z\)-axis. If it makes an angle \(\beta\) with the \(y\)-axis such that \(\sin ^2 \beta=3 \sin ^2 \theta\), what is \(\cos ^2 \theta\) equal to ?

121142 If \(\cos \theta=\frac{\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma}{\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma} \alpha, \beta, \gamma \quad\) are the angles made by a line with the positive directions of the axes of reference, then the measure of \(\theta\) is

121143 If \(P(1,2,3)\) is the given point and \(P N\) is the length of perpendicular from \(P\) on the given
line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}\), then \(P N=\)

121144 If the foot of the perpendicular from the point \(A(-1,4,3)\) on the plane \(P: 2 x+m y+n z=4\), is \(\left(-2, \frac{7}{2}, \frac{3}{2}\right)\), then the distance of the point \(A\) from the plane, measured parallel to a line with direction ratio \(3,-1,-4\), is equal to :

121145 A line makes the same angle \(\theta\) with each of \(x\) axis and \(z\)-axis. If it makes an angle \(\beta\) with the \(y\)-axis such that \(\sin ^2 \beta=3 \sin ^2 \theta\), what is \(\cos ^2 \theta\) equal to ?

121142 If \(\cos \theta=\frac{\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma}{\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma} \alpha, \beta, \gamma \quad\) are the angles made by a line with the positive directions of the axes of reference, then the measure of \(\theta\) is

121143 If \(P(1,2,3)\) is the given point and \(P N\) is the length of perpendicular from \(P\) on the given
line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}\), then \(P N=\)

121144 If the foot of the perpendicular from the point \(A(-1,4,3)\) on the plane \(P: 2 x+m y+n z=4\), is \(\left(-2, \frac{7}{2}, \frac{3}{2}\right)\), then the distance of the point \(A\) from the plane, measured parallel to a line with direction ratio \(3,-1,-4\), is equal to :

121145 A line makes the same angle \(\theta\) with each of \(x\) axis and \(z\)-axis. If it makes an angle \(\beta\) with the \(y\)-axis such that \(\sin ^2 \beta=3 \sin ^2 \theta\), what is \(\cos ^2 \theta\) equal to ?