Question

Two vector having magnitude 6 units and 8 units, the magnitude of resultant of the two vector is :

• A. Exactly 2 units
• B. Exactly 10 units
• C. Exactly 14 units
• D. 0 units, 10 units, or some value between them
• E. 2 units, 14 units, or some value between them

Answer 1

Answer: (E)

2 units, 14 units, or some value between them

The magnitude of resultant vector is $\left|\overrightarrow{R}\right|=\sqrt{P^2+Q^2+2PQcos\theta }$

$-1<cos\theta <1$

Thus $\sqrt{P^2+Q^2-2PQ}<\left|\overrightarrow{R}\right|<\sqrt{P^2+Q^2+2PQ}$

$⟹P-Q\le \left|\overrightarrow{R}\right|\le P+Q$

$⟹2\le \left|\overrightarrow{R}\right|\le 14$