Answer to Question #137050 in Classical Mechanics for Griffith

Question

what is -5.00A + 4.00B

Answer 1

For this question angle and co-ordinate points must be given for A and B.

Let the co-ordinate of A is$(x_1, y_1)$ and angle with positive x axis is$= \theta$

And co-ordinate for the point B is $(x_2,y_2)$ and it is making an angle $\phi$

So, $A=x_1 \cos\theta \hat{i}+y_1\sin\theta\hat{j}$

Similarly, $B=x_2\cos\phi\hat{i}+y_2\sin\phi\hat{j}$

Now it is given $C=-5.00A+4.00B$

Now, substituting the values,

$\Rightarrow C=-5(x_1 \cos\theta \hat{i}+y_1\sin\theta\hat{j})+4.00(x_2\cos\phi\hat{i}+y_2\sin\phi\hat{j})$

$\Rightarrow C=(4x_2\cos\phi-5x_1 \cos\theta)\hat{i}+(4y_2\sin\phi-5y_1\sin\theta)\hat{j})$