Mathematics Vectors & 3D Geometry questions from JEE Main 2008.
If the straight lines $\frac{x-1}{k}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x-2}{3}=\frac{y-3}{k}=\frac{z-1}{2}$ intersect at a point, then the integer $k$ is equal to
The line passing through the points $(5,1, a)$ and $(3, b, 1)$ crosses the $y z-$ plane at the point $\left(0, \frac{17}{2}, \frac{-13}{2}\right)$. Then
The non-zero verctors $\vec{a}, \vec{b}$ and $\vec{c}$ are related by $\vec{a}=8 \vec{b}$ and $\vec{c}=-7 \vec{b}$. Then the angle between $\vec{a}$ and $\overrightarrow{\mathrm{c}}$ is