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NCERT Class 12 · Ch 10 Miscellaneous Exercise · Q10

NCERT Class 12 Maths · Chapter 10 Vector Algebra · Miscellaneous Exercise Question 10

Adjacent sides of a parallelogram are (2,−4,5) and (1,−2,−3). Find unit vector(s) parallel to its diagonal(s) and its area.
Two diagonals of the parallelogram
Two diagonals of the parallelogram

💡 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: For the sum diagonal: ±(3,−6,2)/7. For the other diagonal: ±(1,−2,8)/√69. Area \(11 \sqrt{5}\).
  1. The two diagonal directions are a+b=(3,−6,2), of norm 7, and a−b=(1,−2,8), of norm √69.
  2. Normalize each and retain either sign for parallelism. If the source means the diagonal through their common initial vertex, use a+b.
  3. The area is |a×b|, with a×b=\(\left[\begin{matrix}22\\11\\0\end{matrix}\right]\) and magnitude \(11 \sqrt{5}\).

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