Shown is a 10 by 10 grid, with coordinate axes x and y (Figure 1) . The grid run

Question

Shown is a 10 by 10 grid, with coordinate axes x and y
(Figure 1) .
The grid runs from -5 to 5 on both axes. Drawn on this grid are four vectors, labeled A  through D . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified.

1) What is the x component of A ?

2) What is the y component of A ?

3) What is the y component of B ?

4) What is the x component of C ?

5) In ordered pair notation, write down the components of vector B .

Bx, By =

6) In ordered pair notation, write down the components of vector D

Dx, Dy =

Explanation / Answer

here,

1)

|A| = sqrt(2.5^2 + 3^2)

|A| = 3.91

theta = arctan(3/2.5)

theta = 50.19 degree

Ax = 3.91 * cos(50.19)

Ax = 2.5

the x-component of A is 2.5

2)

|A| = sqrt(2.5^2 + 3^2)

|A| = 3.91

theta = arctan(3/2.5)

theta = 50.19 degree

Ay = 3.91 * sin(39.81)

Ay = 3

the y-component of A is 3

3)

|B| = sqrt(2^2 + 3^2)

|B| = 3.61

theta = arctan(3/2)

theta = 56.31 degree

By = - 3.61 * sin(56.31)

By = -3

the y-component of B is - 3

4)

|C| = sqrt(2^2 + 1^2)

|C| = 2.24

theta = arctan(1/2)

theta = 26.57 degree

Cx = - 2.24 * cos(26.57)

Cx = - 2

the x-component of C is - 2

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