Question

If a=<-3,2,5> and b=<6,2,3>, calculate the equation of the plane parallel to both a and b containing the point P(-1,9,2)

Answer 1

to get the equation of a plane you need a point and a vector normal to the plane

if \(\vec a\) and \(\vec b\) are both parallel to the plane, then their cross product should give the normal vector for the plane

Answer 2

so find the normal vector\[\vec n=\vec a\times\vec b\]

Answer 3

-4i+39j-18k= <-4,39,-18> right?

Answer 4

I think your j component is 45

Answer 5

Would the equation be:
\[-4(x+1)+39(y-9)-18(z-2)\]

Answer 6

\[\vec a\times\vec b=\left|\begin{matrix}\hat i&\hat j&\hat k\\-3&2&6\\6&2&3\end{matrix}\right|=6\hat i+36\hat j-6\hat k-12\hat k-12\hat i+9\hat j=\langle-6,45,-18\rangle\]

Answer 7

You put -3,2,6 instead of -3,2,5

Answer 8

oh ic

Answer 9

\[\vec a\times\vec b=\left|\begin{matrix}\hat i&\hat j&\hat k\\-3&2&5\\6&2&3\end{matrix}\right|=6\hat i+30\hat j-6\hat k-12\hat k-10\hat i+9\hat j=\langle-4,39,-18\rangle\]ok you got it, just be sure top set what you wrote equal to zero

Answer 10

Thanks!

Answer 11

welcome :)