Writing unit vector with the terms in an equation

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Ismita 2024-3-5

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unit_y_vector = (mean_speed_T * mean_speed_N)/(magnitude_U0_mean_RTN)^2 - (mean_speed_R * mean_speed_T)/(magnitude_U0_mean_RTN)^2; 

unit_y_vector = (mean_speed_T * mean_speed_N)/(magnitude_U0_mean_RTN)^2 \hat{R}- (mean_speed_R * mean_speed_T)/(magnitude_U0_mean_RTN)^2 \hat{N};

if first term in the right hand side is along \hat{R} and the second term is along \hat{N}, should I write the unit vectors/expression for those unit vectors with the terms in the equation? Sometimes I see the vector comes from the matrix, we don't need to write. What to do here? I am beginner. Thanks!

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Answer 1

Manikanta Aditya 2024-3-5

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Hey,

Yes, you should write the unit vectors with the terms in the equation. The unit vectors help to specify the direction of each term in the vector equation.

unit_y_vector = \hat{R} * (mean_speed_T * mean_speed_N)/(magnitude_U0_mean_RTN)^2 - \hat{N} * (mean_speed_R * mean_speed_T)/(magnitude_U0_mean_RTN)^2;

Sometimes, when the vector comes from a matrix, the unit vectors are implicit in the matrix’s structure, so they don’t need to be written explicitly. However, as a beginner, it’s a good practice to write them out as it helps you understand the directionality of each term. As you get more comfortable with vectors and matrices, you’ll get a better sense of when you can leave them implicit.

Thanks!