List of top Mathematics Questions on 3D Geometry asked in AP EAMCET

If \( l, m, n \) are the direction cosines of a line that is perpendicular to the lines having the direction ratios \( (1,2,-1) \) and \( (-2,1,1) \), then \( (l+m+n)^2 \) =
The distance of a point \( (2,3,-5) \) from the plane \( \vec{r} \cdot (4i - 3j + 2k) = 4 \) is:
The foot of the perpendicular drawn from a point \( A(1,1,1) \) onto a plane \( \pi \) is \( P(-3,3,5) \). If the equation of the plane parallel to the plane \( \pi \) and passing through the midpoint of \( AP \) is \[ ax - y + cz + d = 0, \] then \( a + c - d \) is:
If a line \( L \) makes angles \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) with the Y-axis and Z-axis respectively, then the angle between \( L \) and another line having direction ratios \( 1,1,1 \) is:
The length of the internal bisector of angle A in \( \triangle ABC \) with vertices \( A(4,7,8) \), \( B(2,3,4) \), and \( C(2,5,7) \) is:
If \((a,b,c)\) are the direction ratios of a line joining the points \((4,3,-5)\) and \((-2,1,-8)\), then the point \(P(a,3b,2c)\) lies on the plane