Answer to Question #158333 in Classical Mechanics for nasia

Question #158333

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. 


1
Expert's answer
2021-01-25T13:55:22-0500

Solution

Given force magnitude


f=6e1+8e2f=6e 1 ​ +8e 2 ​

Angle between e1 and f is =30°

Using basis vector concept

f.e1=(6e1+8e2).e1(6e1+8e2)e1cos30°=6f. 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

e2=436e18=323e14e_2=\frac{4\sqrt{3}-6e_1}{8}=\frac{\sqrt{3}}{2}-\frac{3e_1}{4}


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