Vector Algebra Question 125
Question: If $ \vec{a} $ is a position vector of a point (1, -3) and A is another point (-1, 5), then what are the coordinates of the point B such that $ \overrightarrow{AB}=\vec{a} $ ?
Options:
A) (2, 0)
B) (0, 2)
C) (-2, 0)
D) (0, -2)
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] Let the coordinates of B be (x, y). $ \overset{\to }{\mathop{a}},=i-3j $ P.V. of A is (-1, 5 ) so, $ \overrightarrow{OA}=i+5j, $ $ \overrightarrow{OB}=xi+yj, $
$ \therefore \overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}=\overrightarrow{a} $
$ \Rightarrow (x+1)\hat{i}+(y-5)\hat{j}=\hat{i}-3\hat{j} $
$ \Rightarrow x+1=1 $ and $ y-5=-3 $
$ \Rightarrow x=0 $ and $ y=2 $
$ \therefore $ Coordinates of B are (0, 2 ).
BETA
