Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Vector Algebra · Assertion Reason1 Marksdirection_cosines

Class 12 Maths · Vector Algebra · Assertion Reason #29

Assertion (A): The direction cosines of (1,1,−2) are (1/√6,1/√6,−2/√6). Reason (R): For a nonzero vector (a,b,c), its direction cosines are a/r, b/r, c/r, where r = √(a²+b²+c²).

✅ Step-by-Step Solution

Final Answer: Option (A): Both A and R are true, and R correctly explains A.
  1. The vector has norm √6, and dividing its components by this norm gives the listed cosines.

Master Chapter 10: Vector Algebra

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Vector Algebra.
📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →
← Previous Question
If a + b = i and a = (2,−2,2), find |b|.
Next Question →
Assertion (A): If (a − b) · (a + b) = 0 for nonzero vectors a,b…

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…