Find the coordinates of v → if v → = 2 a → − 3 b → + 4 c → and a → ( 4 ; 1 ) , b → ( 1 ; 2 ) and c → ( 2 ; 7 )

Question

Find the coordinates of             v      →       if             v      →        =  2            a      →        −  3            b      →        +  4            c      →       and             a      →        (  4  ;  1  )  ,            b      →        (  1  ;  2  ) and             c      →        (  2  ;  7  )

gutinyalk · Accepted Answer

Step 1From what I understand,             u      →        (  p  ;  q  ) means that             u      →        is a vector in             R        2   , with coordinates (p, q). So,            v      →        =  2            a      →        −  3            b      →        +  4            c      →        =  2  (  4  ,  1  )  −  3  (  1  ,  2  )  +  4  (  2  ,  7  )  =  (  13  ,  24  )In your notation,             v      →        (  13  ;  24  )

Mylee Underwood · Accepted Answer

Step 1I am supposing that by &quot;find the coordinates&quot; it means cartesian coordinates, and that             a      →        (  4  ;  1  ) is the same as writing:            a      →        =      (                            4                                      1                      )  where 4 is the x component, and 1 is the y component. Then you have a vector determined by three others, but, because you are in the plane             R        2  , it is redundant. So you are looking to reduce the number of &quot;coordinates&quot; (numbers by which you label your vector) to two, which is the minimum. As delta-divine has said, the result would be            v      →        =      (                            13                                      24                      )  which is             v      →        (  13  ;  24  ) in your notation.

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