0
$\begingroup$

Let

$$ a_1 x+b_1 y+c_1 z=d_1\\ a_2 x+b_2 y+c_2 z=d_2\\ a_3 x+b_3 y+c_3 z=d_3 $$

be three planes and it was given that if $d_1=d_2=d_3=1$ then the planes intersect exactly one point. Now my question is if we change the value of $d_1$, $d_2$, $d_3$ like if $d_1=2$, $d_2 =3$, $d_3=4$ do they still intersect at a unique point?

$\endgroup$
0
$\begingroup$

Yes, they will. One way to see this is because the matrix

$$ \left( \begin{array}{ccc} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{array} \right) $$

is invertible.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.