Question

a and b are vectors that are not parallel.
FG = 2a − 3b
-
Choose all of the vectors below which are parallel to
FG.
a-b10a-15
3a-2b-4a+6b 2a + 3b
2a-3b-4a 2a-12b +4a + 3b

Answer 1

Answer:it is a

Step-by-step explanation:

Answer 2

Answer:

$\boxed{\textbf{a}-\dfrac{3}{2}\textbf{b}}$

$\boxed{10 \textbf{a}-15\textbf{b}}$

$\boxed{-4 \textbf{a}+6\textbf{b}}$

$\boxed{2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}}$

Step-by-step explanation:

Given vector:

$\overrightarrow{\rm FG}=2 \textbf{a}-3\textbf{b}$

Two vectors are parallel if one can be written as a scalar multiple of the other.

Therefore, the following vectors are parallel to FG:

$\textbf{a}-\dfrac{3}{2}\textbf{b}=\dfrac{1}{2}(2 \textbf{a}-3\textbf{b})$

$10 \textbf{a}-15\textbf{b}=5(2 \textbf{a}-3\textbf{b})$

$-4 \textbf{a}+6\textbf{b}=-2(2 \textbf{a}-3\textbf{b})$

$2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}=6\textbf{a}-9\textbf{b}=3(2 \textbf{a}-3\textbf{b})$