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NCERT Class 12 · Ch 10 Exercise 10.3 · Q4

NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.3 Question 4

Find the projection of \(\left[\begin{matrix}1\\3\\7\end{matrix}\right]\) on \(\left[\begin{matrix}7\\-1\\8\end{matrix}\right]\).

💡 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: Scalar projection \(\frac{10 \sqrt{114}}{19}\); vector projection \(\left[\begin{matrix}\frac{70}{19}\\- \frac{10}{19}\\\frac{80}{19}\end{matrix}\right]\).
  1. The signed scalar projection is (a·b)/|b|. Here a·b=\(60\) and |b|=\(\sqrt{114}\).
  2. Substitution gives scalar \(\frac{10 \sqrt{114}}{19}\). Multiplying it by b/|b| gives vector projection \(\left[\begin{matrix}\frac{70}{19}\\- \frac{10}{19}\\\frac{80}{19}\end{matrix}\right]\).

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