Vector Algebra Question 268
Question: If a is any vector in space, then
[MP PET 1997]
Options:
A) $ \mathbf{a}=(\mathbf{a},.,\mathbf{i}),\mathbf{i}+,(\mathbf{a},.,\mathbf{j}),\mathbf{j}+,(\mathbf{a},.,\mathbf{k}),\mathbf{k} $
B) $ \mathbf{a}=(\mathbf{a},\times ,\mathbf{i})+,(\mathbf{a},\times ,\mathbf{j}),+,(\mathbf{a},\times ,\mathbf{k}), $
C) $ \mathbf{a}=\mathbf{j},(\mathbf{a},.,\mathbf{i}),+\mathbf{k},(\mathbf{a},.,\mathbf{j}),+,\mathbf{i},(\mathbf{a},.,\mathbf{k}), $
D) $ \mathbf{a}=(\mathbf{a},\times ,\mathbf{i})\times \mathbf{i}+,(\mathbf{a},\times ,\mathbf{j})\times \mathbf{j},+,(\mathbf{a},\times ,\mathbf{k})\times \mathbf{k}, $
Show Answer
Answer:
Correct Answer: A
Solution:
- Let $ \mathbf{a}=a_1\mathbf{i}+a_2\mathbf{j}+a_3\mathbf{k}, $ then $ \mathbf{a}.\mathbf{i}=a_1, $ $ \mathbf{a}.\mathbf{j}=a_2, $ $ \mathbf{a}.\mathbf{k}=a_3 $
$ \therefore ,\mathbf{a}=(\mathbf{a},.,\mathbf{i})\mathbf{i}+(\mathbf{a},.,\mathbf{j})\mathbf{j}+(\mathbf{a},.,\mathbf{k})\mathbf{k} $ .
BETA
