# Need some help with vectors and planes!

#### Kalbaan

##### New member
Hey!

I just joined the forum, but would like to get some help with 2D&3D vectors and dot product. I missed some classes due to a bad illness and now can't get the hang of it at all..
Would appriciate it alot, if someone could explain me how to solve these 5 exercises.

#### Deveno

##### Well-known member
MHB Math Scholar
Some hints:

a) Can you think of a way to use the dot product here?

b) If two vectors are of equal magnitude, but opposite direction, their vector sum is 0. Why is this relevant?

c) We have the 3 equations:

$3\lambda + 3\mu + 1 = x$

$-\lambda + 2\mu - 1 = y$

$4\lambda - 2 = z$

By multiplying equations (1) and (2) by suitable integers, can you eliminate $\mu$? Then try to use that equation and equation 3 to eliminate $\lambda$.

d) Such a line should be parallel to $v$, right?

e) Think about what the direction vectors of such a plane have to be....

#### Kalbaan

##### New member
Thanks alot! You made my week mate!
Got the hang of them with your hints and my teachers powerpoint shows.

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
There is another way of finding an equation of a plane in (c) and (e): an equation of the plane perpendicular to $(A,B,C)$ and passing through $(x_0.y_0,z_0)$ is $A(x-x_0)+B(y-y_0)+C(z-z_0)=0$, or $Ax+By+Cz+(-Ax_0-By_0-Cz_0)=0$.