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Need some help with vectors and planes!

Kalbaan

New member
Dec 17, 2013
2
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.
LinearAlgebra.png
 

Deveno

Well-known member
MHB Math Scholar
Feb 15, 2012
1,967
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
Dec 17, 2013
2
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
Jan 30, 2012
2,492
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 $Ax+By+Cz+(-Ax_0-By_0-Cz_0)=0$.