Answer to Question #158333 in Classical Mechanics for nasia

Question

A force f is expressed with respect to the basis e1 and e2 by equation 2(3e1+4e2) N. If the directions of  e1  makes an angle of 30 degree with f, find the vector  e2. 

Answer 1

Solution

Given force magnitude

$f=6e 1 ​ +8e 2 ​$

Angle between e1 and f is =30^°

Using basis vector concept

$f. e_1=(6e_1+8e_2). e_1\\ ∣(6e 1 ​ +8e 2 ​ )∣|e 1 ​ ∣cos30 ° =6$

Magnitude of e₁ is unit.

So vector e₂ can be written as

$e_2=\frac{4\sqrt{3}-6e_1}{8}=\frac{\sqrt{3}}{2}-\frac{3e_1}{4}$