List of top Mathematics Questions on Coordinate Geometry asked in CBSE CLASS XII

Let three toys A, B and C be placed in the same straight line. If the position vectors of A, B and C are $55\hat{i} - 2\hat{j}$, $5\hat{i} + 8\hat{j}$ and $a\hat{i} - 52\hat{j}$ respectively, find the exact numerical value of '$a$'.
If the area of \( \Delta ABC \) with vertices \( A(3, 1) \), \( B(-2, 1) \) and \( C(0, k) \) is \( 5 \) sq. units, then values of \( k \) are :
There is a triangular park in the society. The park is divided into two sections as shown in the figure. The vertices of the triangular park ABC are A(0, 4), B(\(-2\), 0) and C(3, 0). Based on the above information, answer the following questions :
A man needs to hang two lanterns on a straight wire whose end points have coordinates A (4, 1, -2) and B (6, 2, -3). Find the coordinates of the points where he hangs the lanterns such that these points trisect the wire AB.
If P is a point on the line segment joining $(3, 6, -1)$ and $(6, 2, -2)$ and the $y$-coordinate of P is 4, then its $z$-coordinate is :
(a) Find the point Q on the line \( \frac{2x + 4}{6} = \frac{y + 1}{2} = \frac{-2z + 6}{-4} \) at a distance of \( \frac{\sqrt{5}}{2} \) from the point \( P(1, 2, 3) \).
A man needs to hang two lanterns on a straight wire whose end points have coordinates A (4, 1, -2) and B (6, 2, -3). Find the coordinates of the points where he hangs the lanterns such that these points trisect the wire AB.