Vector Algebra Question 205
Question: Given three vectors $ \vec{a}=6\hat{i}-3\hat{j},\hat{b}=2\hat{i}-6\hat{j} $ and $ \vec{c}=-2\hat{i}+21\hat{j} $ such that $ \overrightarrow{\alpha }=\vec{a}+\vec{b}+\vec{c} $ . Then the resolution of the vector $ \overrightarrow{\alpha } $ into components with respect to $ \vec{a} $ and $ \vec{b} $ is given by
Options:
A) $ 3\vec{a}-2\vec{b} $
B) $ 3\vec{b} $ $ - $ $ 2\vec{a} $
C) $ 2\vec{a}-3\vec{b} $
D) $ \vec{a}-2\vec{b} $
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ \vec{\alpha }=\vec{a}+\vec{b}+\vec{c}=6\hat{i}+12\hat{j} $ Let $ \vec{\alpha }=x\vec{a}+y\vec{b}\Rightarrow 6x+2y=6 $ And $ -,3x-6y=12 $
$ \therefore x=2,y=-3 $
$ \therefore \vec{\alpha }=2\vec{a}-3\vec{b} $
BETA
