Question

If \(|\vec a|=2,\ |\vec b|=5\) and \(|\vec a\times\vec b|=8\), then \(|\vec a\cdot\vec b|\) is equal to :

• A. 6
• B. 4
• C. 3
• D. 5

Hint:

Use \(|\vec a\times\vec b|=|\vec a||\vec b|\sin\theta\) to get \(\cos\theta\).

Answer 1

The Correct Option is A

\(|\vec a\times\vec b|=|\vec a||\vec b|\sin\theta\Rightarrow 8=10\sin\theta\Rightarrow\sin\theta=\frac45\).
\(|\cos\theta|=\sqrt{1-\frac{16}{25}}=\frac35\).
\(|\vec a\cdot\vec b|=|\vec a||\vec b||\cos\theta|=10\times\frac35=6\).
Answer: (1) 6