Question

Consider three vectors A⃗ ,B⃗ and C⃗ all lying in the xy plane. Vector A⃗ has length 6.2 and makes an angle of 131 degrees with the x-axis. Vector B⃗ has length 7.3 and makes an angle of 32 degrees with the x-axis. The vector D⃗ =A⃗ +B⃗ +C⃗ has x-component DX = 3.1 and y-component DY = 6.7 .A) Find the magnitude of the vector C⃗ .B) Find the angle in degrees that vector C⃗ makes measured counterclockwise from the x-axis.

Answer 1

Answer:

A) 2.09

B) -62.09°

Explanation:

If D = A+B+C  then C = D - A - B

Converting both A and B to rectangular coordinates, we get:

A = [-4.07 , 4.68]    and    B = [6.19 , 3.87]

Replacing these values we can get the x and y components of C:

C = [0.98 , -1.85]

Its module is:

$|C| = \sqrt{0.98^2+(-1.85)^2}=2.09$

Its angle is:

$\alpha _c = atan(-1.85/0.98) = -62.09\°$