Vector Algebra Question 284
Question: If the position vectors of the points A, B, C be $ \mathbf{a},\ \mathbf{b} $ , $ 3\mathbf{a}-2\mathbf{b} $ respectively, then the points A, B, C are
[MP PET 1989]
Options:
A) Collinear
B) Non-collinear
C) Form a right angled triangle
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- Here $ \overrightarrow{AB}=\mathbf{b}-\mathbf{a} $ and $ \overrightarrow{AC}=(3\mathbf{a}-2\mathbf{b})-(\mathbf{a})=-2(\mathbf{b}-\mathbf{a}) $ Therefore, it is of the form $ \overrightarrow{AB}=m\overrightarrow{AC}. $ Hence A, B, C are collinear.
BETA
