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If the position vector of a point P is given by r = (2t, 3t, 4t), find the coord

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Question: If the position vector of a point P is given by r = (2t, 3t, 4t), find the coordinates of P when t = 1.

Options:

  1. (2, 3, 4)
  2. (1, 1, 1)
  3. (0, 0, 0)
  4. (2, 4, 6)

Correct Answer: (2, 3, 4)

Solution: 

Substituting t = 1, r = (2*1, 3*1, 4*1) = (2, 3, 4).

If the position vector of a point P is given by r = (2t, 3t, 4t), find the coord

Practice Questions

Q1
If the position vector of a point P is given by r = (2t, 3t, 4t), find the coordinates of P when t = 1.
  1. (2, 3, 4)
  2. (1, 1, 1)
  3. (0, 0, 0)
  4. (2, 4, 6)

Questions & Step-by-Step Solutions

If the position vector of a point P is given by r = (2t, 3t, 4t), find the coordinates of P when t = 1.
Correct Answer: (2, 3, 4)
  • Step 1: Identify the position vector of point P, which is given as r = (2t, 3t, 4t).
  • Step 2: Understand that 't' is a variable that can take different values.
  • Step 3: We need to find the coordinates of point P when t = 1.
  • Step 4: Substitute t = 1 into the position vector: r = (2*1, 3*1, 4*1).
  • Step 5: Calculate each component: 2*1 = 2, 3*1 = 3, and 4*1 = 4.
  • Step 6: Write the final coordinates of point P as r = (2, 3, 4).
  • Position Vectors – Understanding how to evaluate a position vector given a parameter.
  • Substitution – Applying the correct value of the parameter to find specific coordinates.
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