The angle subtended by a vector A = i - j with the x-axis is:
Correct answer: D. 315 degrees
- A. 45 degrees
- B. 135 degrees
- C. 225 degrees
- D. 315 degrees
Explanation
To find the angle subtended by a vector A with the x-axis, we can use the inverse tangent function. Given vector: A = i - j Where 'i' and 'j' are the unit vectors along the x-axis and y-axis respectively. The angle θ subtended by vector A with the x-axis can be calculated using the formula: θ = tan-1(Ay / Ax) Where Ay is the y-component of vector A and Ax is the x-component of vector A. In this case, Ay = -1 and Ax = 1 Putting values in the above formula, we get: θ = tan-1(-1/1) = tan-1(-1) = -45° We can convert the angle to its positive equivalent: θ = 360° - |-45°| = 360° - 45° θ = 315°
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About Rectangular Components
A vector is resolved into perpendicular horizontal and vertical components using trigonometric relations, usually as Ax = A cos θ and Ay = A sin θ when θ is measured from the horizontal. Questions involve signs in different quadrants, reconstructing a resultant from components, and using components to analyse equilibrium.
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