If the lines $\overset{⃗}{r} = (\hat{i}+m\hat{j}+3\hat{k})+λ(2\hat{i}+3\hat{j}+4\hat{k})$ and $\overset{⃗}{r} = (4\hat{i}+\hat{j})+μ(5\hat{i}+m\hat{j}+\hat{k})$ intersect each other, then m =

Question

Let the lines l₁: $\frac{x+5}{3} = \frac{y+4}{1}=\frac{z−α}{−2}$ and l₂: 3x + 2y + z – 2 = 0 = x – 3y + 2z - 13 be coplanar. If the point P(a, b, c) on l₁ is nearest to the point Q(- 4, -3, 2), then |a| + |b|+|c| is equal to

Answer 1

Step 1: Unknowns
The k component of the second line is $\mu$ and of the first is $3 + 4\lambda$.

Step 2: Solve two equations
The i and k components give $\lambda = \mu = -1$.

Step 3: Remaining
The j components: $m - 3 = 1 - m$, so $m = 2$. Option (C).

Final Answer:
Option (C). \[ \boxed{2} \]

If the lines \(\overset{⃗}{r} = (\hat{i}+m\hat{j}+3\hat{k})+λ(2\hat{i}+3\hat{j}+4\hat{k})\) and \(\overset{⃗}{r} = (4\hat{i}+\hat{j})+μ(5\hat{i}+m\hat{j}+\hat{k})\) intersect each other, then m =

Show Hint

The Correct Option is C

Solution and Explanation

Top Questions on Coplanarity of Two Lines

Questions Asked in MHT CET exam