A. Equation of the line passing through the point (1, 2, 3) and parallel to the vector $3\hat i+2\hat j-2\hat k$ is $\frac{x-1}{3}=\frac{y-2}{2}=\frac{z-3}{-2}$

B. Equation of line passing through (1, 2, 3) and parallel to the line given by $\frac{x+3}{3}=\frac{4-y}{5}=\frac{z+8}{6}$ is $\frac{x-1}{3}=\frac{y-2}{5}=\frac{z-3}{6}$

C. Equation of line passing through the origin and (5, -2, 3) is 2-3

D. Equation of plane passing through the point (1, 2, 3) and perpendicular to the line with direction ratio's 2, 3, -1 is $2(x-1)-3(y-2)-1(z-3)=0$

E. Equation of plane with intercepts 2, 3 and 4 on x, y and z-axis respectively is $2x + 3y+4z = 1$.

Choose the correct answer from the options given below:

A only

The correct answer is option (1) → A only

(A) Equation of line will be $\frac{x-1}{3}=\frac{y-2}{2}=\frac{z-3}{-2}$

(Correct Statement)

(B) Given line → $\frac{x+3}{3}=\frac{4-y}{5}=\frac{z+8}{6}$

$⇒ \frac{x+3}{3}=\frac{y-4}{-5}=\frac{z+8}{6}$

direction ratios → 3, -5, 6

So line passing through (1, 2, 3)

$\frac{x-1}{3}=\frac{y-2}{-5}=\frac{z-3}{6}$

(Incorrect statement)

(C) Vague statement "2 - 3" is not form of a line

(Incorrect statement)

(D) Eq. of plane through (1, 2, 3) and perpendiculat to (2, 3, -1) vector is $2(x-1)+3(y-2)-1(x-3)=0$

(Incorrect statement)

(E) Equation of plane with intercepts 2, 3, 4 is $\frac{x}{2}+\frac{y}{3}+\frac{z}{4}=1$

(Incorrect statement)

⇒ Only statement A is correct.