Login/Sign Up
Home » Find the coordinates of the point where the line joining A(3, 4, 1) and B(5, 1, 6) crosses the xy-plane.
Find the coordinates of the point where the line joining A(3, 4, 1) and B(5, 1, 6) crosses the xy-plane.
CBSE | Class 11 | Exercise 26C | Maths | RS Aggarwal | Three Dimensional Geometry
Find the coordinates of the point where the line joining A(3, 4, 1) and B(5, 1, 6) crosses the xy-plane.

Answer:

Let the plane XY divides the points A(3,4,1) and B(5, 1, 6) in ratio k:1.

On XY plane, Z co- ordinate of every point be zero.

Formula –

Using the above formula,

\begin{array}{l} = \left( {\frac{{k \times 5 + 1 \times 3}}{{k + 1}},\frac{{k \times 1 + 1 \times 4}}{{k + 1}},\frac{{k \times 6 + 1 \times 1}}{{k + 1}}} \right)\\ {\frac{{k \times 6 + 1 \times 1}}{{k + 1}} = 0 \end{array}

6k + 1 = 0

k = -1/6

The ratio is 1:6 externally in XZ plane which divides the line joined from points A and B.

i

More Material