Which of the following statements are true?

(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector $3\hat i+ 2\hat j - 8\hat k$ is
$\vec r= (5\hat i+2\hat j-4\hat k) +λ(3\hat i + 2\hat j −8\hat k)$
(B) Vector form of the equation of line $\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}$ is $\vec r=(5\hat i-4\hat j+6\hat k) +λ(3\hat i+7\hat j + 2\hat k)$
(C) The direction cosines of z-axis are (1, 1, 0).
(D) If a line has direction ratios 2, -1, -2, then its direction cosines are -2/3, -1/3, -2/3.

Choose the correct answer from the options given below:

(A) and (B) only

The correct answer is Option (3) → (A) and (B) only

(A) Line through point $(5,2,-4)$ parallel to $\vec{d} = 3\hat{i} + 2\hat{j} - 8\hat{k}$: $\vec{r} = (5\hat{i} + 2\hat{j} - 4\hat{k}) + \lambda(3\hat{i} + 2\hat{j} - 8\hat{k})$ → Correct

(B) Given symmetric form: $\frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2}$

Vector form: $\vec{r} = (5\hat{i} - 4\hat{j} + 6\hat{k}) + \lambda(3\hat{i} + 7\hat{j} + 2\hat{k})$ → Correct

(C) Direction cosines of z-axis: $(0,0,1)$ → Not (1,1,0) → Incorrect

(D) Direction ratios: 2, -1, -2

Magnitude: $\sqrt{2^2 + (-1)^2 + (-2)^2} = \sqrt{4+1+4} = 3$

Direction cosines: $(2/3, -1/3, -2/3)$ → Not (-2/3, -1/3, -2/3) → Incorrect