What is the equation of the line passing through the points (1, 2, 3) and (4, 5,
Practice Questions
Q1
What is the equation of the line passing through the points (1, 2, 3) and (4, 5, 6)?
x = 1 + 3t, y = 2 + 3t, z = 3 + 3t
x = 1 + t, y = 2 + t, z = 3 + t
x = 1 + t, y = 2 + 2t, z = 3 + 3t
x = 1 + 3t, y = 2 + 2t, z = 3 + t
Questions & Step-by-Step Solutions
What is the equation of the line passing through the points (1, 2, 3) and (4, 5, 6)?
Step 1: Identify the two points given: Point A (1, 2, 3) and Point B (4, 5, 6).
Step 2: Calculate the direction ratios by subtracting the coordinates of Point A from Point B: (4 - 1, 5 - 2, 6 - 3) = (3, 3, 3).
Step 3: Use the direction ratios (3, 3, 3) to write the parametric equations of the line.
Step 4: The parametric equations are formed as follows: x = x1 + at, y = y1 + bt, z = z1 + ct, where (x1, y1, z1) is Point A and (a, b, c) are the direction ratios.
Step 5: Substitute the values: x = 1 + 3t, y = 2 + 3t, z = 3 + 3t.
