Vector Algebra Question 335
Question: If $ a,.,i=a,.,(i+j)=a,.,(i+j+k) $ , then a =
[EAMCET 2002]
Options:
A) i
B) k
C) j
D) i + j + k
Show Answer
Answer:
Correct Answer: A
Solution:
- Let $ \mathbf{a}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k} $ . Then $ \mathbf{a},.,\mathbf{i}=(x\mathbf{i}+y\mathbf{j}+z\mathbf{k}),.,\mathbf{i}=x $ and $ \mathbf{a},.,(\mathbf{i}+\mathbf{j})=x+y $ and $ \mathbf{a},.,(\mathbf{i}+\mathbf{j}+\mathbf{k})=x+y+z $ $ \because $ Given that $ x=x+y=x+y+z $ Now $ x=x+y,\Rightarrow y=0 $ and $ x+y=x+y+z\Rightarrow z=0 $ Hence $ x=1 $ ;
$ \therefore \mathbf{a}=\mathbf{i} $ .
BETA
