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.

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:

Its angle is:

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