Question

Two vectors X and Y are added together. Which of the following statements could be true?
I. The resultant magnitude is smaller than X.
II. The resultant magnitude is larger than Y.
III. The resultant direction is the same as either X or Y

• A. I only
• B. II only
• C. I and III only
• D. II and III only
• E. I, II, and III

Answer 1

Answer: (E)

I, II, and III

(i) If the angle between vectors $X$ and $Y$ is ${180}^o$, then resultant can be smaller than $X$.

(ii) If the angle between vectors $X$ and $Y$ is $0^o$, then resultant can be larger than $Y$.

(iii) If the angle between vectors $X$ and $Y$ is $0^o$ or ${180}^o$, then the direction of resultant can be same as either $X$ or $Y$.

Therefore, all statements could be true.