Which statement is incorrect regarding the vector A = 2i + 2j + 3k ?
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Answer: D. Has magnitude -2
Explanation
Vector magnitude is calculated by taking the square root of the sum of squared components. For vector A, the components squared give four plus four plus nine equaling seventeen. The true magnitude equals the square root of seventeen, which clearly contradicts a magnitude of minus two. Vector components represent the projections of the vector along the three Cartesian coordinate axes. The magnitude of any physical vector represents a scalar length and must be non-negative. Direction angles of vectors are found using components divided by the total vector magnitude.
Checking vector magnitudes ensures that physical calculations yield realistic and valid measurements. Negative magnitudes are physically impossible for spatial vectors representing distance or force. Spatial vector analysis is fundamental for solving three-dimensional physics and engineering problems. Having a direction of fourty-five degrees with the x-axis is mathematically plausible for this vector. A magnitude of two is listed incorrectly in some options but the negative value is definitively wrong. Direction angles with coordinate axes are standard geometric properties calculated in vector algebra.
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