A linear algebra solve found zero solutions, weirdly [closed]

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Let E, P, QA be points of a 3D space, let a*QAx+b*QAy+c*QAz==d ensures that QA is in a certain plane. Let |E P| and |E QA| be the same line. Why did my attempt to find QA found zero solutions?

#!/usr/bin/env python
# coding: utf-8

# In[1]:


var('a b c d')


# In[2]:


var('Ex Ey Ez')


# In[3]:


E=vector([Ex,Ey,Ez])


# In[4]:


var('Px Py Pz')


# In[5]:


P=vector([Px,Py,Pz])


# In[6]:


var('k QAx QAy QAz')


# In[7]:


QA=vector([QAx,QAy,QAz])


# In[14]:


solve([E-P==k*(E-QA), a*QAx+b*QAy+c*QAz==d], [k, QAx, QAy, QAz])