Consider the following statements : I. \( (\vec{a} \times \vec{b}) \cdot \vec{c} + (\vec{b} \times \vec{c}) \cdot \vec{a} = (\vec{c} \times \vec{a}) \cdot \vec{b} \) II. \( \{(\vec{a} \times \vec{b}) \times (\vec{b} \times \vec{c})\} \cdot \vec{b} = 1 \) Which of the statements given above is/are correct ?
For the next two (02) items that follow : Let \( \vec{a} \times \vec{b} = \vec{c} \) and \( \vec{b} \times \vec{c} = \vec{a} \)
- A. I only
- B. II only
- C. Both I and II
- D. Neither I nor II ✓
Correct Answer: D. Neither I nor II
Explanation
Statement I reduces to 2[\vec{a}, \vec{b}, \vec{c}] = [\vec{a}, \vec{b}, \vec{c}], which is impossible since the scalar triple product is non-zero. Statement II reduces to |\vec{a}|^2, which is not necessarily 1. Both are false.
Related questions on Vector Algebra
- PQRS is a parallelogram. If \vec{PR}=\vec{a} and \vec{QS}=\vec{b}, then what is \vec{PQ} equal to?
- Let \vec{a} and \vec{b} are two unit vectors such that \vec{a}+2\vec{b} and 5\vec{a}-4\vec{b} are <strong>PERPENDICULAR</strong>. Wh...
- Let \vec{a}, \vec{b} and \vec{c} be unit vectors lying on the same <strong>COPLANAR</strong> plane. What is $\{(3\vec{a}+2\vec{b})\tim...
- What are the values of x for which the angle between the vectors 2x^{2}\hat{i}+3x\hat{j}+\hat{k} and \hat{i}-2\hat{j}+x^{2}\hat{k} is ...
- The position vectors of vertices A, B and C of triangle ABC are respectively \hat{j}+\hat{k}, 3\hat{i}+\hat{j}+5\hat{k} and $3\h...