What is the equation of the line passing through the points (1, 2, 3) and (4, 5, 6)?
Practice Questions
1 question
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
Direction ratios = (3, 3, 3), hence the line equation is x = 1 + 3t, y = 2 + 3t, z = 3 + 3t.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the equation of the line passing through the points (1, 2, 3) and (4, 5, 6)?
Solution: Direction ratios = (3, 3, 3), hence the line equation is x = 1 + 3t, y = 2 + 3t, z = 3 + 3t.
Steps: 5
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.
