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Unformatted text preview: vectors are [ ) and [
. Part (b)
Following the same approach as part (a) :
1.
2.   √
→ ( ) () √ √ √ Hence, the two possible vectors are and
[ √ .
[ √ Part (c)
A point lies on the plane perpendicular to 1. (
2. (
plane.
3. ( )(
)( ) )( ) if . Hence: so ( ) is on the plane.
) is NOT on the
so ( )
so ( ) is NOT on the plane. Part (d)
Vector that is parallel to the line along which P and Q intersect if is perpendicular to
both and . To find such a vector we have to find one of the many solutions for the
following system of equation: Using rref of the corresponding augmented matrix we get:
, and is free In order to get one of many possible solutions let’s fix
and . Hence we get: . Part (e)
( ) ( )
( (
)( ) ( ) ) According to the definition of perpendicular vectors one of many possible answers is:
( )...
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 Fall '13
 KFOURY
 Algorithms

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