Vectors
Ratio of magnitudes from unit vectors
MJAT_TS8_P2
Grade 12
Question:
If $\hat{u}$ and $\hat{v}$ are non-collinear unit vectors with $|\hat{u}+\hat{v}+2(\hat{u}\times\hat{v})|=2$, then $\dfrac{|\hat{u}-\hat{v}|}{|\hat{u}\times\hat{v}|}$ equals:
Step-by-Step Solution
Key Concept: Let $\theta$ be angle between $\hat{u}$ and $\hat{v}$. $|\hat{u}+\hat{v}+2\hat{u}\times\hat{v}|^2=1+1+4\sin^2\theta+2\cos\theta=4$.
Ratio $=\mathbf{2}$. Answer: **B**.
Correct Answer: B