Find the coordinates of v → if v → = 2 a → − 3...

Ellen Chang

Ellen Chang

Answered

2022-07-07

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

Answer & Explanation

gutinyalk

gutinyalk

Expert

2022-07-08Added 11 answers

Step 1
From 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

Mylee Underwood

Expert

2022-07-09Added 3 answers

Step 1
I am supposing that by "find the coordinates" 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 "coordinates" (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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