List of top Mathematics Questions on 3D Geometry asked in LPUNEST

If \(\lambda(3\mathbf{i} + 2\mathbf{j} - 2\mathbf{k})\) is a unit vector, then the value(s) of \(\lambda\) are:
If \((1,-2,-2)\) and \((0,2,1)\) are direction ratios of two lines, then the direction cosines of a line perpendicular to both the lines are:
The plane x - 2y + 3z = 17 divides the line joining the points (-2, 4, 7) and (3, -5, 8) in the ratio
The ratio of the distances from the points (1,–1,3) and (3,3,3) to plane \(5x+2y-7z+9=0\) is
If \[ \int \frac{1}{(x+100)\sqrt{x+99}}\,dx = f(x)+c \] then $f(x)=$
Evaluate: \[ \int_{0}^{\pi} \frac{x\sin x}{1+\cos^2 x}\,dx \]