hw2-solutions

Based on these two properties we can for the

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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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