Question

If the points $(0,1,-2),(3,\lambda ,-1)$ and $(\mu ,-3,-4)$ are collinear, the point on the same line is

• A. $(12,9,2)$
• B. $(1,-1,-2)$
• C. $(5,-3,4)$
• D. $(0,0,0)$

Answer 1

Answer: (A)

$(12,9,2)$

We know condition of collinearity,

$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$

We have points $(0,1,-2),(3,\lambda ,-1)and(\mu ,-3,-4)$

$\frac{x-0}{3-0}=\frac{y-1}{\lambda -1}=\frac{z+2}{-1+2}.........\left(1\right)$

Since $(\mu ,-3,-4)$ is collinear , so it satisfy equation (1)

taking y and z coordinates,

$\frac{-3-1}{\lambda -1}=\frac{-4+2}{-1+2}$

$\lambda =3$

Now equation (1) becomes

$\frac{x-0}{3-0}=\frac{y-1}{3-1}=\frac{z+2}{-1+2}.........\left(2\right)$

Option (A) (12,9,2) satisfy equation (2).

Therefore option (A) is correct.