Vector Algebra Question 27
Question: ABCD a parallelogram, $A_1$ and $B_1$ are the midpoints of sides $B C$ and $C D$, respectively. If $\overrightarrow{A A_1}+\overrightarrow{A B_1}=\lambda \overrightarrow{A C}$, then $\lambda$ is equal to
Options:
A) $ \frac{1}{2} $
B) 1
C) $ \frac{3}{2} $
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] Let P. V of A, B and D be $ \vec{0},,\vec{b} $ and $ \vec{d} $ , respectively. Then P.V. of C, $ \vec{c}=\vec{b}+\vec{d} $ . Also P.V. of $ A_1=\vec{b}+\frac{{\vec{d}}}{2} $ and P.V. of $ B_1 $ $ =\vec{d}+\frac{{\vec{b}}}{2}\Rightarrow \overrightarrow{AA_1}=\frac{3}{2}(\vec{b}+\vec{d})=\frac{3}{2}\overrightarrow{AC} $
BETA
