Find the ratio in which the plane x-2y+3z =17 divides the line joining the points (-2,4,7) and (3,-5,8) Also obtain - Maths - Limits and Derivatives

Question

Find the ratio in which the plane x-2y+3z =17 divides the line
joining the points (-2,4,7) and (3,-5,8) Also obtain the
coordinates of the point of intersection

Priyanka Kedia · Accepted Answer

Suppose that the line AB, joining the points A (-2, 4, 7) and B(3, -5, 8) is divided by the planes x-2y+3z = 17 at the point

in the ratio k: 1, internally Then,

Since

lies on the plane x-2y+3z=17, we have,

Or

Therefore, the required ratio 3: 10, internally, Further, putting the above value of k in the expressions for a, b, and c, we get,

Hence, the coordinates of the point of intersection are

Find the ratio in which the plane x-2y+3z =17 divides the line joining the points (-2,4,7) and (3,-5,8).Also obtain the coordinates of the point of intersection.