Vector Algebra Question 216
Question: Let $ \vec{a} $ , $ \vec{b} $ and $ \vec{c} $ be the three vectors having magnitudes 1, 5 and 3, respectively, such that the angle between $ \vec{a} $ and $ \vec{b} $ is $ \theta $ and $ \vec{a}\times (\vec{a}\times \vec{b})=\vec{c} $ Then tan $ \theta $ is equal to
Options:
A) 0
B) 2/3
C) 3/5
D) ¾
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] $ \vec{a}\times (\vec{a}\times \vec{b})=\vec{c}\Rightarrow \overrightarrow{| a |}| \vec{a}\times \vec{b} |=\overrightarrow{| c |} $ $ (\therefore \vec{a}\bot (\vec{a}\times \vec{b})) $ $ 1(1\times 5)sin\theta =3\Rightarrow sin\theta =\frac{3}{5}\Rightarrow \tan \theta =\frac{3}{4} $
BETA
