# What represents the vector: 2a-5b

by imy786
Tags: 2a5b, represents, vector
 P: 322 1. The problem statement, all variables and given/known data if vector : line a starts from co-ordinates (0,0) and ends at (5,3) line b starts from co-ordinates (0,0) and ends at (1,2) What represents the vector: 2a-5b 2. Relevant equations 3. The attempt at a solution I was initially thinking of computing Pythagorus theorem for each of the two lines. for Line a = square root of (25+9) = square root of 24 for line b = square root of (1+4) = square root of 5 2a-5b = 2 x square root of 6 - 5 x square root of 5 which doesn't seem right...tips would be nice please. need an answer in the form of an x and y co-ordinate
 P: 1,195 Not sure of what 2a means. Does it mean a vector starting at (0,0) and ending at (10,6)? Does 5b mean a vector starting at (0,0) and ending at (5,10)?
 P: 322 anyone else? tips or hints?
HW Helper
Thanks
P: 9,675

## What represents the vector: 2a-5b

2a means twice the vector a, a vector in the same line as a and of twice length. In coordinates, a=(5,3) and the vector is represented by an arrow starting at (0,0) and ending at (5,3). 2a=(10,6), 5b=(5,10)
2a-5b means the difference between 2a and 5b. When you add (subtract) vectors, you add (subtract) the components.

ehild
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,705 Most importantly, there is nothing here that asks you to find the length of any vector. Do not use the Pythagorean theorem!
 P: 322 so if 2a=(10,6), 5b=(5,10) and 2a-5b then 10-5 = 5 6-10 = -4 therefore= 2a-5b=(5,-4)
 P: 322 thanks guys especially echild- whats your qualifications?
 HW Helper Thanks P: 9,675 You are welcome. ehild

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