Mathematics · JEE | VECTOR ALGEBRA

Consider the following statements regarding vectors in component form: (A) The scalar components of a vector \( \vec{r} = x\hat{i} + y\hat{j} + z\hat{k} \) are \( x, y, z \). (B) Two vectors \( \vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k} \) and \( \vec{b} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k} \) are collinear if and only if \( \frac{b_1}{a_1} = \frac{b_2}{a_2} = \frac{b_3}{a_3} \). (C) The scalar product of two vectors is always a vector quantity. (D) If \( \theta \) is the angle between two nonzero vectors \( \vec{a} \) and \( \vec{b} \), then \( \vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}|\cos\theta \). Which of the above statements are correct?

1. A
   (A), (B) and (D) only
2. B
   and (C) only
3. C
   (B), (C) and (D) only
4. D
   (A), (B), (C) and (D)