If the vertices of a triangle ABC are $A(1, 2, 1)$, $B(4, 2, 3)$ and $C(2, 3, 1)$, then the equation of the median passing through the vertex $A$, is

If the points (-1, -1, 2), (2, m, 5) and (3, 11, 6) are collinear, then m equals

If a line makes angles $\alpha, \beta, \gamma$ with the positive directions of $x$-axis, $y$- axis and $z$-axis respectively, then $sin^2 \alpha + sin^2 \beta + sin^2 \gamma$ is equal to

The line $\frac{x+2}{3} = \frac{y+3}{5} = \frac{z-6}{4}$ passes through (a, 2, c). The value of a and c are:

Let $L_1$ and $L_2$ be two lines, represented as,

$L_1: \vec{r} = \hat{i} + \hat{j} + \lambda(2\hat{i} - \hat{j} + \hat{k})$ and $L_2: \vec{r} = 2\hat{i} + \hat{j} - \hat{k} + \mu(4\hat{i} - 2\hat{j} + 2\hat{k})$, where $\lambda$ and $\mu$ are scalars. Then which of the following are true?

(A) $L_1$ is perpendicular to $L_2$.

(B) $L_1$ is parallel to $L_2$.

(C) $L_1$ passes through the point (1, 1, 0)

(D) $L_2$ passes through the point (2, 1, -1)

Choose the correct answer from the options given below:

A line in space is uniquely determined if

(A) It passes through a given point and has a given direction.

(B) It passes through two given points.

(C) It passes through a given point.

(D) It has a given direction.

Choose the correct answer from the options given below:

The Cartesian equation of a line is $6x-2=3y+1=2z-2$. Then its vector from is: