The intersection of the planes defined by
$V \bullet \begin{pmatrix} 8 \ 1 \ -12 \end{pmatrix} = 35$
and
$V \bullet \begin{pmatrix} 6 \ 7 \ -9 \end{pmatrix} = 70$
is a line. $V$ is a vector. Find an equation of this line.

Please please help, thank you!

Question

The intersection of the planes defined by
$V \bullet \begin{pmatrix} 8 \ 1 \ -12 \end{pmatrix} = 35$
and
$V \bullet \begin{pmatrix} 6 \ 7 \ -9 \end{pmatrix} = 70$
is a line. $V$ is a vector. Find an equation of this line.

Please please help, thank you!

ganeshie8 · Answer

As a start, convince yourself that the line of intersection of the given two planes is perpendicular to the normal vectors of the planes http://www.mathematics-online.org/inhalt/aussage/aussage515/img5.png

ganeshie8 · Answer

next you may take the cross product of the normal vectors to find the direction vector of the intersecting line

zmudz · Answer

@ganeshie8 I'm not sure how to do that, though. Would you mind elaborating? Thank you so much!

zmudz · Answer

never mind, solved it! Thank you so much!