Question

Q15 The angle between two vectors is 60°, and the magnitude of vectors is same i.e. F, then resultant vector will be, a) 14.6F c) d)414 b) 2.32F d)732F​

Answer 1

Given: The angle between two vectors is 60°, and the magnitude of vectors is same i.e. F.

To find: Resultant of these vectors

Explanation: Let the vectors be a and b. Then,

Magnitude of a = F

Magnitude of b = F

Angle between a and b = 60°

Let the resultant of these vectors be denoted by r.

The formula used to find resultant of two vectors is:

${r}^{2} = {a}^{2} + {b}^{2} + 2ab \cos(60)$

${r}^{2} = {F}^{2} + {F}^{2} + 2 {F}^{2} \times \frac{1}{2}$

( since cos 60° = 1/2)

${r}^{2} = 2 {F}^{2} + {F}^{2}$

${r}^{2} = 3 {F}^{2}$

$r = \sqrt{3} F$

r = 1.732 F

Therefore, the resultant of these vectors is 1.732 F.