Question

Six vectors \( \vec{a},\vec{b},\vec{c},\vec{d},\vec{e},\vec{f} \) have magnitudes and directions shown. Which statement is true? 

• A. \( \vec{b}+\vec{e}=\vec{f} \)
• B. \( \vec{b}+\vec{c}=\vec{f} \)
• C. \( \vec{d}+\vec{c}=\vec{f} \)
• D. \( \vec{d}+\vec{e}=\vec{f} \)

Hint:

Vector diagrams:
Follow head-to-tail rule.
Match direction and magnitude.

Answer 1

The Correct Option is D

Concept: Use head-to-tail vector addition.

Step 1: Observe directions
- \( \vec{d} \): upward.
- \( \vec{e} \): leftward.
Resultant points diagonally up-left.

Step 2: Compare with \( \vec{f} \)
Vector \( \vec{f} \) is slanted up-left.

Step 3: Conclusion
\[ \vec{d} + \vec{e} = \vec{f} \]