Question

Find the coordinates of the point where the line through A (9, 4 , 1) and B (5, 1, 6) crosses X axis ?

Answer 1

To find the coordinates of the point where the line through points A(9, 4, 1) and B(5, 1, 6) crosses the X-axis, we need to determine the value of the X-coordinate when the Y and Z coordinates are both zero.

Let's find the equation of the line passing through points A and B. The direction vector of the line can be found by subtracting the coordinates of B from A:

AB = [5 - 9, 1 - 4, 6 - 1] = [-4, -3, 5]

Now we can write the parametric equations for the line:

x = 9 - 4t y = 4 - 3t z = 1 + 5t

To find the point where the line crosses the X-axis, we need to solve for the values of t when both y and z are zero.

Setting y = 0 and z = 0:

4 - 3t = 0 1 + 5t = 0

Solving these equations simultaneously, we find:

t = 3/4 t = -1/5

Since we're looking for the point where the line intersects the X-axis, we are only concerned with the X-coordinate. Substituting the value of t into the equation for x, we get:

x = 9 - 4(3/4) = 9 - 3 = 6

Therefore, the coordinates of the point where the line crosses the X-axis are approximately (6, 0, 0).