# The vectors A, B, C and R are related by A + B + C = R with Ax = 3, Ay = 2.5, Bx = 4.2, By = -2.2, Rx = 3.5 and Ry = 3.5. What is the magnitude of C

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You should remember the formula that allows you to find the magnitude of the vector `barC` such that:

`|barC| = sqrt(C_x^2 + C_y^2)`

Hence, you should find the components of vector barC.

You may write the vector `bar R ` such that:

`bar R = R_x*bar i + R_y*bar j`

Substituting 3.5 for `R_x` and `R_y` yields:

`bar R = 3.5*bar i + 3.5*bar j`

You may write the sum of vectors such that:

`barA + barB + barC = barR`

`A_x*bari + A_y*bar j + B_x*bari + B_y*bar j + C_x*bari + C_y*bar j =3.5*bar i + 3.5*bar j`

`bar i*(A_x + B_x + C_x) + bar j*(A_y + B_y + C_y) = 3.5*bar i + 3.5*bar j`

`bar i*(3 +4.2 + C_x) + bar j*(2.5-2.2 + C_y) = 3.5*bar i + 3.5*bar j`

You need to set the equations `3 + 4.2 + C_x = 3.5` and `2.5 - 2.2 + C_y = 3.5` equal such that:

`3 + 4.2 + C_x = 3.5 =gt C_x = 3.5 - 3- 4.2`

`C_x = -3.7`

`2.5 - 2.2 + C_y = 3.5 =gt C_y = 3.2`

Hence, substituting -`3.7` for `C_x` and `3.2` for `C_y` yields:

`|barC| = sqrt((-3.7)^2 + (3.2)^2)`

`|barC| = sqrt(13.69+10.24) =gt |barC| = sqrt23.93`

`|barC| = 4.89`

**Hence, evaluating the magnitude of vector barC under given conditions yields `|barC| = 4.89.` **

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