The lines x-2-1-y-3-1-z-4-k and x-1-k-y-4-2-z-5-1 are coplanar ifA- k -1 or -1B- k -0 or -3C- k -3 or -3D- k -0 or -1

The correct option is B k =0 or 3Two lines are coplanar if x_2 x_1 amp; y_2 y_1 amp; z_2 z_1 a_1 amp; b_1 amp; c_1 a_2 amp; b_2 amp; c_2 = ...

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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to be on the Same Plane

The lines x-2...

Question

The lines $\frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{- k} a n d \frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1}$ are coplanar if

k =1 or -1

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k =0 or -3

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k =3 or -3

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k =0 or -1

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Solution

The correct option is B k =0 or -3
Two lines are coplanar if $∣ ∣ ∣ ∣ \begin{matrix} x_{2} - x_{1} & y_{2} - y_{1} & z_{2} - z_{1} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} \end{matrix} ∣ ∣ ∣ ∣ = 0$

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Similar questions

Q. The line

\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. if

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

Q. 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, if

Q. The line

\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 if

Q. 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 if

k

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The lines x−21=y−31=z−4−kandx−1k=y−42=z−51 are coplanar if

The correct option is B k =0 or -3Two lines are coplanar if ∣∣ ∣∣x2−x1y2−y1z2−z1a1b1c1a2b2c2∣∣ ∣∣=0

The lines $\frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{- k} a n d \frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1}$ are coplanar if

The correct option is B k =0 or -3
Two lines are coplanar if $∣ ∣ ∣ ∣ \begin{matrix} x_{2} - x_{1} & y_{2} - y_{1} & z_{2} - z_{1} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} \end{matrix} ∣ ∣ ∣ ∣ = 0$