Question

Find the coordinates of the point where the line through the points A(3, 4, 1) and B(5, 1, 6) crosses the XZ plane. Also find the angle which this line makes with the XZ plane.

Answer 1

Let P (a, b, g) be the point at which the given line crosses the XZ plane.

Now the equation of given line AB is

Since P \((\alpha, \beta, \gamma)\) lies on line (i)

Also P \((\alpha, \beta, \gamma)\) lie on XZ plane, i.e., y = 0 (0x + 1y + 0z = 0)

Hence, the co-ordinates of required point P is

\(\therefore\) Co-ordinate of required point is \((\frac{17}{3},0,\frac{23}{3})\)

Let q be the angle made by line AB with XZ plane.