OAB is a triangle.
[tex]\overrightarrow{OA} = 3a + 5b[/tex]
[tex]\overrightarrow{OB} = 4a - b[/tex]
Write [tex]\overrightarrow{AB}[/tex] in terms of [tex]a[/tex] and [tex]b[/tex].
Fully simplify your answer.
Answer (1)
To find A B in terms of a and b , we can use the following vector subtraction rule:
A B = OB − O A
Given:
O A = 3 a + 5 b
OB = 4 a − b
Substitute these into the equation:
A B = ( 4 a − b ) − ( 3 a + 5 b )
Apply the distributive property and rearrange:
Start by distributing the negative sign: 4 a − b − 3 a − 5 b
Combine like terms:
The a terms: 4 a − 3 a = 1 a
The b terms: − b − 5 b = − 6 b
Thus, the simplified form of A B is:
A B = a − 6 b
This expresses the vector A B in terms of a and b .
