If the lines (x+1/2) = (y-1/1) = (z+1/3) and (x+2/2) = (y-k/3) =(z/4) are coplanar, then the value of k is :

Question

If the lines (x+1/2) = (y-1/1) = (z+1/3) and (x+2/2) = (y-k/3) =(z/4) are coplanar, then the value of k is : (A) (11/2) (B)  - (11/2) (C) (9/2) (D)  - (9/2)

Tardigrade Admin · Accepted Answer

Two given planes are coplanar, if |-2-(-1)&k-1&0-(-1) 2&1&3 2&3&4|= 0 ⇒ |-1&k-1&1 2&1&3 2&3&4| = 0 ⇒ (- 1) (4 - 9) - (k - 1) (8 - 6) + 6 - 2 = 0 ⇒ k = (11/2)

Q. If the lines $\frac{x + 1}{2} = \frac{y - 1}{1} = \frac{z + 1}{3}$ and $\frac{x + 2}{2} = \frac{y - k}{3} = \frac{z}{4}$ are coplanar, then the value of k is :

$\frac{11}{2}$

$- \frac{11}{2}$

$\frac{9}{2}$

$- \frac{9}{2}$

Two given planes are coplanar, if
$∣ ∣ - 2 - (- 1) 22 k - 1 13 0 - (- 1) 34 ∣ ∣ = 0$
$\Rightarrow ∣ ∣ - 1 22 k - 1 13 134 ∣ ∣ = 0$
$\Rightarrow (- 1) (4 - 9) - (k - 1) (8 - 6) + 6 - 2 = 0$
$\Rightarrow k = \frac{11}{2}$

Q. If the lines 2x+1​=1y−1​=3z+1​ and 2x+2​=3y−k​=4z​ are coplanar, then the value of k is :

211​

−211​

29​

−29​