Math Is Fun Forum

beefjerky

Member

Registered: 2008-03-17

Posts: 3

Math Lines and Vectors help Q3

Please provide all steps and state the answer, please and thank you.

1.

Determine parametric equations for the plane through the points A(2, 1, 1), B(0, 1, 3), and C(1, 3, −2).

2.

Determine a vector equation for the plane that is parallel to the xy -plane and passes through the point (4, 1, 3).

Mikael

Member

Registered: 2008-04-10

Posts: 3

Re: Math Lines and Vectors help Q3

question 2 is a favorite problem in high school vectors. i hope my small answer would be enough

Qu:
what is the vector equation of a Plane ( containing points P, say) which is parallel to xy plane and passes through point A (4,1,3) ??

well
(1) as the plane is parallel to the xy plane, then... it is perpendicular  to the z axis!!!
so, the normal vector is the k vector.

normal vector                   n  =   c   k,   

where c is a number and k is the vector along the z axis.

(2) if the plane passes through point A(4,1,3) then from anywhere in the plane, take a point P.  We can contruct a vector lying on the plane itself

                                     AP  =  OP - OA 

which is at right angles to the normal vector of the plane.

(3) as   vectors  n  and AP are at right angles to each other, their dot product is zero.

So,                              n. AP =  0

the vector equation is:

                                  k. (  r -   OA) =  0