What is the equation of the line passing through the points (1, 2, 3) and (4, 5,

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Question: What is the equation of the line passing through the points (1, 2, 3) and (4, 5, 6)?

Options:

Correct Answer: x = 1 + 3t, y = 2 + 3t, z = 3 + 3t

Solution:

Direction ratios = (3, 3, 3), hence the line equation is x = 1 + 3t, y = 2 + 3t, z = 3 + 3t.

What is the equation of the line passing through the points (1, 2, 3) and (4, 5, 6)?

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.

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