Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Vector Algebra · Short Answer2 Markssection_formula

Class 12 Maths · Vector Algebra · Short Answer #52

Collinear points A,B,C have position vectors a,b,c, with B between A and C. If AC = (5/4)AB as directed vectors, express c in terms of a,b.
AC = 5/4 AB; points placed to the stated ratio
AC = 5/4 AB; points placed to the stated ratio

✅ Step-by-Step Solution

Final Answer: c = (5b − a)/4.
  1. Write AC = c − a and AB = b − a.
  2. The condition gives c − a = (5/4)(b − a), so 4c − 4a = 5b − 5a.
  3. Therefore 4c = 5b − a and c = (5b − a)/4.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Write AC = c − a and AB = b − a.
  • [1 mark] The condition gives c − a = (5/4)(b − a), so 4c − 4a = 5b − 5a.
  • [0.5 marks] Therefore 4c = 5b − a and c = (5b − a)/4.

Master Chapter 10: Vector Algebra

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Vector Algebra.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
X,Y have position vectors 3a + b and a − 3b. Find the position…
Next Question →
If |v| = a, find |v × i|² + |v × j|² + |v × k|².

More Practice Questions in Vector Algebra

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

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…