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IAT IISER2026MathematicsVector Algebra

Consider the points A(4 i + j + 3 k ) , B(2 j ) and C(-4 i + 3 j - 3 k ) . Which of the following statements is TRUE?

Options

  1. AAB BC = i + j + k .
  2. BAB + 3 BC is perpendicular to AC .
  3. CAB , BC and CA are mutually perpendicular.
  4. DA , B and C are collinear.

Correct answer

D. A , B and C are collinear.

Step-by-step solution

Position vectors of the points are given as A = 4 i + j + 3 k , B = 2 j , and C = -4 i + 3 j - 3 k . The vectors AB and BC are calculated as follows: AB = B - A = (0 - 4) i + (2 - 1) j + (0 - 3) k = -4 i + j - 3 k BC = C - B = (-4 - 0) i + (3 - 2) j + (-3 - 0) k = -4 i + j - 3 k Since AB = BC , the vectors are parallel and share the common point B . Therefore, the points A , B , and C are collinear. Answer: A , B and C are collinear.

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