Question 205: Motion in 2D & Vectors

Question

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

Accepted Answer

Given : $$\left( {\overrightarrow {{F_1}}  + \overrightarrow {{F_2}} } \right) \bot \left( {\overrightarrow {{F_1}}  - \overrightarrow {{F_2}} } \right)$$
$$\left( {\overrightarrow {{F_1}}  + \overrightarrow {{F_2}} } \right).\left( {\overrightarrow {{F_1}}  - \overrightarrow {{F_2}} } \right) = 0$$
$$F_1^2 - F_2^2 - \overrightarrow {{F_1}} .\overrightarrow {{F_2}}  + \overrightarrow {{F_2}} .\overrightarrow {{F_1}}  = 0$$
$$ \Rightarrow F_1^2 = F_2^2$$   (i.e. F
1
, F
2
are equal to each other in magnitude.)

Answer

are equal to each other

Answer

are equal to each other in magnitude

Answer

are not equal to each other in magnitude

Answer

cannot be predicted.

Motion in 2D & Vectors

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

Choose the correct answer: