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Three vectors A, B and C are such that

A = B + C and their magnitudes are 5, 4 and 3 respec-
tively. Find the angle between A and C.

Please answer with explanation

User Nissar
by
6.9k points

1 Answer

2 votes

Since the magnitudes satisfy the identity for right triangles


A^2=B^2+C^2

we deduce that B and C are perpendicular, and that ABC is a right triangle (see picture).

So, we can get the angle between A and C using the sine theorem:


\frac{A}{\sin(\hat{A})}=\frac{B}{\sin(\hat{B})}

And we have


A=5,\quad B=4,\quad \hat{A}=90

So, we have


\sin(\hat{B})=\frac{B\sin(\hat{A})}{A}=(4\sin(90))/(5)=(4)/(5)

Which implies


\hat{B}=\arcsin\left((4)/(5)\right)\approx 53.13

Three vectors A, B and C are such that A = B + C and their magnitudes are 5, 4 and-example-1
User Markus Fischer
by
6.9k points