The straight line passing through $(-3, 6)$ and the midpoint of the line segment joining the points $(4, -5)$ and $(-2, 9)$ has an inclination of:

For what values of $a$ and $b$ are the intercepts cut off on the coordinate axes by the line $ax + by + 8 = 0$ equal in length but opposite in sign to those cut off by the line $2x - 3y + 6 = 0$ on the axes?

If the slope of a line is $2$ and it makes an intercept of $-4$ on the $y$-axis,then its equation is:

$A$ line passes through the point $(1, 2)$ and makes an angle of $60^{\circ}$ with the $x$-axis. The coordinates of the points on this line at a distance of $3$ units from the point $(1, 2)$ are:

$A$ straight line passes through the point $A(3, 4)$ such that its intercept between the axes is bisected at $A$. Find its equation.

Let $u = \hat{i} - 2\hat{j}$ and $v = -3\hat{i} + 5\hat{j}$. Consider three points $P, Q,$ and $R$ having position vectors $-\frac{1}{7}\hat{i}$,$-\frac{1}{4}\hat{j}$,and $-2\hat{i} + 3\hat{j}$ respectively. Among these,the points on the line segment passing through $u$ and $v$ are