Question

Find the horizontal and vertical components of the following vectors shown in the diagram. In all cases, assume that up and right are positive directions and that the diagonals are 45°.

Answer 1

The horizontal and vertical component of vector A is -3 and 0 respectively.

The horizontal and vertical component of vector B is 0 and 3 respectively.

The horizontal and vertical component of vector C is 0 and 6 respectively.

The horizontal and vertical component of vector D is 4 and 0 respectively.

The horizontal and vertical component of vector E is 3.54 and 3.54 respectively.

The horizontal and vertical component of vector F is -3.54 and -3.54 respectively.

The horizontal an vertical component of each vector

The horizontal and vertical component of each vector is calculated as follows;

Vector A

$A_x = Acos (\theta) = 3 \times cos(180) = -3\\\\A_y = A sin(\theta) = 3 \times sin(180) = 0$

Vector B

$B_x = 3 \times cos(90) = 0\\\\B_y = 3 \times sin(90) = 3$

Vector C

$C_x = 6 \times cos(90) = 0\\\\C_y = 6 \times sin(90) = 6$

Vector D

$D_x = 4 \times cos(0) = 4\\\\D_y = 4 \times sin(0) = 0$

Vector E

$E _x = 5 \times cos (45) = 3.54 \\\\E_y = 5 \times sin(45) = 3.54$

Vector F

$F_x = 5 \times cos(225) = -3.54\\\\F_y = 5 \times sin(225) = -3.54$

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