Published by:
CGP EDU Academic Team
Published on: September 12, 2026
For any three non zero vector 
, 
and 
if 
. 
= 
. 
then it may be possible that 
≠ 
.
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Identify the given vectors as \( A, B, C \) and the condition involving these vectors.
Step 2: Use the properties of vector addition and the relationship that in a vector space, if \( A + B + C = D \), then the vectors are linearly independent if they do not lie on the same plane.
Step 3: Given that \( A \), \( B \), and \( C \) are non-zero vectors, we analyze the condition provided in the question stating that \( D \) might not equal zero.
Step 4: Conclude that if \( A \), \( B \), and \( C \) do not sum up to form a dependent relationship, the final conclusion aligns with option A. Therefore, the answer is A.
Step 2: Use the properties of vector addition and the relationship that in a vector space, if \( A + B + C = D \), then the vectors are linearly independent if they do not lie on the same plane.
Step 3: Given that \( A \), \( B \), and \( C \) are non-zero vectors, we analyze the condition provided in the question stating that \( D \) might not equal zero.
Step 4: Conclude that if \( A \), \( B \), and \( C \) do not sum up to form a dependent relationship, the final conclusion aligns with option A. Therefore, the answer is A.
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