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.

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lcmendozaf lcmendozaf · Answer 1 · 2019-11-09T14:23:37+01:00

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:

[tex]|C| = \sqrt{0.98^2+(-1.85)^2}=2.09[/tex]

Its angle is:

[tex]\alpha _c = atan(-1.85/0.98) = -62.09\°[/tex]

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andromache andromache · Answer 2 · 2022-02-08T15:12:33+01:00

A) The magnitude of the vector is 2.09

B) The angle should be -62.09°

In the case when D = A+B+C then C = D - A - B

Now

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

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

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

C = [0.98 , -1.85]

Its module is:

[tex]= \sqrt{0.98^2+ (-1.85)^2}[/tex]

= 2.09

b. Now the angle should be

[tex]= tan(-1.85\div 0.98)[/tex]

= -62.09°

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