Vinod Singh and Shweta Pawar Solutions for Chapter: Three Dimensional Geometry, Exercise 1: Classical Thinking

If the line through the points $\left(3,1,2\right)$ and $\left(4,\lambda ,0\right)$ is parallel to the line through the points $\left(1,2,1\right)$ and $\left(2,3,-1\right)$, find $\lambda$

The points $\left(5,2,4\right), \left(6,-1,2\right)$ and $\left(8,-7,k\right)$ are collinear if $k$ is equal to

The value of $\lambda$ for which the points $\left(-2,4,\lambda \right), \left(3,-6,-8\right), \left(1,-2,-2\right)$ are collinear is

If the direction cosines of two lines are $\frac{1}{\sqrt{6}}, \frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}}$ and $\frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-1}{\sqrt{6}}$, respectively, then the acute angle between them is

If direction ratios of two lines are $5,-12,13$ and $-3,4,5$, then the angle between them is

If the coordinates of the points $A, B, C, D$ be $\left(1,2,3\right),\left(4,5,7\right),\left(-4,3,-6\right)$ and $\left(2,9,2\right)$, respectively, then the angle between the lines $AB$ and $CD$ is

If the angle between the lines whose direction ratios are $2, -1, 2$ and $a, 3, 5$ be $45°$, then $a=$

If the coordinates of the points $P$ and $Q$ are $\left(1,-2,1\right)$ and $\left(2,3,4\right)$ and $O$ is the origin, then