The distance of the point $A(3, -4, 5)$ from the plane $2x + 5y - 6z = 16$ measured along the line $\frac{x}{2} = \frac{y}{1} = \frac{z}{-2}$ is

The vector equation of the plane passing through the point $i + 2j - k$ and perpendicular to the line of intersection of the planes $r \cdot (3i - j + k) = 1$ and $r \cdot (i + 4j - 2k) = 2$ is

If a line $L$ is the line of intersection of the planes $2x + 3y + z = 1$ and $x + 3y + 2z = 2$. If line $L$ makes an angle $\alpha$ with the positive $X$-axis,then the value of $\sec \alpha$ is

Let $\vec{a}, \vec{b}, \vec{c}$ be three non-coplanar vectors and $L$ be the line passing through the points $\vec{a}-\vec{b}+\vec{c}$ and $\vec{b}-\vec{c}$. If $\pi$ is a plane passing through the points $2\vec{a}-\vec{b}, 2\vec{b}-\vec{c}$ and $2\vec{c}-\vec{a}$, then the point of intersection of $L$ and $\pi$ is

Let $L$ be the line of intersection of the planes $2x + 3y + z = 1$ and $x + 3y + 2z = 2$. If $L$ makes an angle $\alpha$ with the positive direction of the $x$-axis,then $\cos \alpha$ is:

The centre of the circle given by $r \cdot (i + 2j + 2k) = 15$ and $|r - (j + 2k)| = 4$ is