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Choose the correct option.
For any three vectors a⃗, b⃗ and c⃗, Statement 1: a⃗ · (b⃗ × c⃗) is a scalar. Statement 2: a⃗ · (b⃗…
For any three vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$,
Statement 1: $\vec{a} \cdot (\vec{b} \times \vec{c})$ is a scalar.
Statement 2: $\vec{a} \cdot (\vec{b} \times \vec{c}) = \vec{a} \cdot (\vec{c} \times \vec{b})$
Which one of the following is correct?
- aStatement 1 is true and Statement 2 is false.
- bStatement 2 is true and Statement 1 is false.
- cBoth the statements are true.
- dBoth the statements are false.
Answer
Answer
Correct option: a
Answer: (a) Statement 1 is true and Statement 2 is false.
$\vec{a}\cdot(\vec{b}\times\vec{c})$ is a dot product, hence a scalar. But $\vec{c}\times\vec{b}=-\vec{b}\times\vec{c}$, so $\vec{a}\cdot(\vec{c}\times\vec{b})=-\vec{a}\cdot(\vec{b}\times\vec{c})$, and Statement 2 is false.