Vinod Singh and Shweta Pawar Solutions for Chapter: Three Dimensional Geometry, Exercise 4: Evaluation Test

If $\theta$ is the acute angle between two intersecting straight lines, one having direction cosines $l_1, m_1, n_1$ and the other having direction cosines $l_2, m_2, n_2$, then ${\sin }^2\theta =$

$A\left(2,3,7\right), B\left(-1,3,2\right), C\left(p,5,r\right)$ are vertices of $∆ABC$. If the median through $A$ is equally inclined to the co-ordinate axes, then the values of $p$ and $r$ are

If $A\left(3,2,6\right), B\left(1,4,5\right), C\left(3,5,3\right)$ are the vertices of triangle $ABC$, then $m\angle ABC=$

The angle between the lines whose direction cosines are given by the equation $6mn-2nl+5lm=0, 3l+m+5n=0$ is

If $l, m, n$ are direction cosines of a line, then the maximum value of $lm+mn+nl$ is

If the point $\left(a,2,3\right), \left(3,b,7\right)$ and $\left(-3,-2,-5\right)$ are collinear, the values of $a$ and $b$, respectively are

The direction cosines of a line, which is perpendicular to both the lines whose direction ratios are $1,-1,0$ and $2,-1,1$, are

Which of the following represents direction cosines of a line which is equally inclined to the axes?