- #1

Aurelius120

- 168

- 16

- Homework Statement
- Find the value of K for which the given lines are coplanar

- Relevant Equations
- NA

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So I tried to solve it this way:

The equations of the lines in vector form are

So I tried to solve it this way:

The equations of the lines in vector form are

$$(x-2)\hat i+(y-3)\hat j+(z-4)\hat k=\lambda (\hat i+\hat j-K\hat k)$$

$$(x-1)\hat i+(y-4)\hat j+(z-5)\hat k=\mu (K\hat i+2\hat j+1\hat k)$$

**Since the lines are some real multiple of the vectors,**

For coplanarity $$(\hat i+\hat j-K\hat k)\times (K\hat i+2\hat j+1\hat k)=0$$

Therefore, ##2-k=0; -k^2-1=0; 1+2k=0##

**So no solutions should exist, right?**

But the book and some websites solve it thus

But the book and some websites solve it thus

*So where and why did I go wrong??*