23 If a⇀ b⇀ are unit vectors, then angle between a⇀ b⇀ for 3a⇀- b⇀ - Maths - Vector Algebra

Question

23   I f   a ⇀ &   b ⇀   a r e
  u n i t   v e c t o r s ,   t h e n   a n g l
e   b e t w e e n   a ⇀ &   b ⇀
    f o r   3 a ⇀ -   b ⇀  
  t o   b e   a   u n i t   v e c t o r
  i s         ( A ) 90 0    
                 
                ( B ) 30 0
        ( C ) 45 0        
                 
            ( D ) 60 0

Koka Sri Lakshmi Divya Sai · Accepted Answer

Dear Student

Given a→ and b→ are unit vectors⇒a→ =1and  b→ =1we knowa→
b→=a→b→cosθ    where θ is the angle between a→ and b→also given3a→-b→=1Squaring on both sides3a→-b→2=1⇒3a→2+b→2-23a→
b→=1⇒3+1-23a→b→cosθ=1⇒3+1-23cosθ=1⇒23cosθ=3⇒cosθ=323=32=cos300⇒θ=300∴The angle between a→ and b→ is 300

Regards

23 . I f a ⇀ & b ⇀ a r e u n i t v e c t o r s , t h e n a n g l e b e t w e e n a ⇀ & b ⇀ f o r 3 a ⇀ - b ⇀ t o b e a u n i t v e c t o r i s ( A ) 90 0 ( B ) 30 0 ( C ) 45 0 ( D ) 60 0

$23 . I f \overset{⇀}{a} & \overset{⇀}{b} a r e u n i t v e c t o r s, t h e n a n g l e b e t w e e n \overset{⇀}{a} & \overset{⇀}{b} f o r \sqrt{3} \overset{⇀}{a} - \overset{⇀}{b} t o b e a u n i t v e c t o r i s (A) 90^{0} (B) 30^{0} (C) 45^{0} (D) 60^{0}$