Question 4: Find the magnitude and direction of vector represented by the following pair of components. (a) Ax = -2.3 cm, Ay = 4.1 cm (b) Ax = 3.9 m, Ay = -1.8 m.

Solution

(a) Given: x-component, A_{x} = -2.3 cm y-component of A, A_{y} = 4.1 cm

Asked Magnitude and direction of A

Solution Since x-component is negative and y-component is positive, the vector A lies in the second quadrant of the reference axes. See the diagram.

Formulae

Put values in formula (1) to find the magnitude of A.

Put values in formula (2) to find the direction of A.

However, this angle is with the negative x-direction. To find angle of the vector along positive x-direction, we subtract it from 180°. See also the diagram. Therefore,

θ = 180° – 60.7° = 119.3° Answer (a)

(b)Given: x-component, A_{x} = 3.9 m y-component, A_{y} = -1.8 m

Put values in formula (1) to find the magnitude of A

Put values in formula (2) to find the direction of A

Now y-axis is negative and x-axis is positive. This means the vector lies in the fourth quadrant. θ is to be subtracted from 360°. Therefore, θ = 360° – 24.8° = 335.2°.

See diagram below.

Did you know?

When both component of a vector are positive, the vector lies in 1st quadrant.

When x-component is –ve and y- component is +ve, the vector lies in the 2nd quadrant.

When both components are –ve the vector lies in 3rd quadrant.

When both components are –ve the vector lies in 3rd quadrant.

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