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NCERT Class 12 · Ch 10 Exercise 10.1 · Q5

NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.1 Question 5

True/false: (i) a and −a are collinear; (ii) collinear vectors always have equal magnitudes; (iii) equal magnitudes imply collinearity; (iv) collinear vectors of equal magnitude are equal.

💡 Concept Hints

  1. Write the vector components and identify the required direction or geometric relation.
  2. Use the magnitude, dot-product, cross-product or section formula that matches the requested quantity.

✅ Step-by-Step Solution

Final Answer: (i) True; (ii),(iii),(iv) False.
  1. (i) −a is the scalar multiple −1 times a. (ii) i and 2i are collinear but have different lengths.
  2. (iii) i and j have equal length but perpendicular directions. (iv) i and −i are collinear with equal length but are different vectors.

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