Condition for Two Lines to be on the Same Plane

Q.

Two lines $L_1:x=5,\frac{y}{3-\alpha }=\frac{z}{-2}$ and $L_2:x=\alpha ,\frac{y}{-1}=\frac{z}{2-\alpha }$ are coplanar. Then, $\alpha$ can take value(s)

1. 1

2. 2

3. 3

4. 4

Q.

If the lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$ and$\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are coplanar, then k can have

1. any value

2. exactly one value

3. exactly two values

4. exactly three values

Q.

Two lines $L_1:x=5,\frac{y}{3-\alpha }=\frac{z}{-2}$ and $L_2:x=\alpha ,\frac{y}{-1}=\frac{z}{2-\alpha }$ are coplanar. Then, $\alpha$ can take value(s)

1. 1

2. 2

3. 3

4. 4

Q.

If the straight lines $\frac{x-1}{2}=\frac{y+1}{K}=\frac{z}{2}$ and $\frac{x+1}{5}=\frac{y+1}{2}=\frac{z}{K}$ are coplanar, then the plane(s) containing these two lines is/are

1. y +2z = - 1

2. y + z = - 1

3. y - z = - 1

4. y - 2z = - 1

Q. The number of distinct real values of $\lambda$ for which the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{{\lambda }^2}$ and $\frac{x-3}{1}=\frac{y-2}{{\lambda }^2}=\frac{z-1}{2}$ are coplanar is:

1. $3$
2. $4$
3. $1$
4. $2$

Q.

If the straight lines $\frac{x-1}{2}=\frac{y+1}{K}=\frac{z}{2}$ and $\frac{x+1}{5}=\frac{y+1}{2}=\frac{z}{K}$ are coplanar, then the plane(s) containing these two lines is/are

1. y +2z = - 1

2. y + z = - 1

3. y - z = - 1

4. y - 2z = - 1