NCERT Class 12 · Ch 10 Exercise 10.2 · Q15
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.2 Question 15
Find R dividing P=i+2j−k, Q=−i+j+k in ratio PR:RQ=2:1 (i) internally (ii) externally.
💡 Concept Hints
- Write the vector components and identify the required direction or geometric relation.
- Use the magnitude, dot-product, cross-product or section formula that matches the requested quantity.
✅ Step-by-Step Solution
Final Answer: (i) \(\left[\begin{matrix}- \frac{1}{3}\\\frac{4}{3}\\\frac{1}{3}\end{matrix}\right]\); (ii) \(\left[\begin{matrix}-3\\0\\3\end{matrix}\right]\)
- Internal section formula gives R=(1P+2Q)/(2+1)=\(\left[\begin{matrix}- \frac{1}{3}\\\frac{4}{3}\\\frac{1}{3}\end{matrix}\right]\).
- External section formula gives R=(2Q−P)/(2−1)=\(\left[\begin{matrix}-3\\0\\3\end{matrix}\right]\). It lies beyond Q on the oriented line from P to Q.
Master Chapter 10: Vector Algebra
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Vector Algebra.
← Previous Question
Show i+j+k is equally inclined to the positive coordinate axes.
Next Question →Find the midpoint position vector for P(2,3,4), Q(4,1,−2).
Related Questions in Vector Algebra
Class 12 Vector Algebra · Mcq Single Correct
Find |a × b|² + (a · b)².
Class 12 Vector Algebra · Mcq Single Correct
Find the area of triangle OAB, where OA = (1,2,3) and OB = (−3,−2,1).
Class 12 Vector Algebra · Mcq Single Correct
For nonzero vectors a,b with angle θ ∈ [0,π], when is a · b ≥ 0?
Class 12 Vector Algebra · Mcq Single Correct
For a vector a, find (a · i)i + (a · j)j + (a · k)k.
Class 12 Vector Algebra · Mcq Single Correct
Which vector has magnitude 9 and the same direction as (1,−2,2)?
Class 12 Vector Algebra · Mcq Single Correct
Find the position vector dividing the segment from 2a − 3b to a + b internally in the ratio…