JEE Main 2015MathematicsVector AlgebraMediumMCQ

JEE Main 2015 — Vector Algebra Question with Solution

JEE Main 2015 (10 Apr Online)

Question

Let a→and b→ be two unit vectors such that a→+b→=3. If c→=a→+2b→+(a→×b→) , then 2c→ is equal to:

Choose an option

Show full solutionCorrect option: D
Correct answer
D55

Step-by-step explanation

As a→ +b→ = 3

Squaring both the sides 

a→2+ b→2+2a→⋅b→=3

1+1+2 ⋅1⋅1⋅cos⁡θ=3

2cosθ=1

cosθ=12

θ=60°

∴   Angle between a→ and b→ is 60o

Now, 

| c → | = | a →  + 2 b →  + 3( a →  ×  b → )|

Squaring both the sides 

| c → | 2  = | a →   | 2 + 4| b → | + 9| a →  ×  b → | 2 + 4 a → .( b → )+3 a → .( a →  ×  b → )+6 b → .( a →  ×  b → )

| c → | 2  =1+4+9 sin 2 θ+4cosθ+0+0

| c → | 2  =5+9. 3 4 +4. 1 2 = 55 4

∴  2 | c → | = 55  

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About this question

This is a previous-year question from JEE Main 2015, covering the Vector Algebra chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.