What represents the vector: 2a-5b

[imy786]

Homework Statement

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

Homework Equations

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

 

[LawrenceC]

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)?

 

[imy786]

anyone else? tips or hints?

 

[ehild]

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

 

[HallsofIvy]

Most importantly, there is nothing here that asks you to find the length of any vector. Do not use the Pythagorean theorem!

 

[imy786]

so if 2a=(10,6), 5b=(5,10)

and 2a-5b

then

10-5 = 5

6-10 = -4

therefore= 2a-5b=(5,-4)

 

[imy786]

thanks guys especially echild- what's your qualifications?

 

[ehild]

You are welcome.

ehild