Find the orthogonal decomposition of vector b = 9, 0, 0 with respect to vector a = 4, −5, 0 . (Your instructors prefer angle bracket notation < > for vectors.)

The orthogonal componentes of with respect to are and , respectively.

Step-by-step explanation:

Let be and , the component of parallel to is found by the following expression:

Where means for dot product and is the unit vector of , which is determined by:

Where is the norm of , which can be found by Pythagorean Theorem.

The vector of parallel to vector is now determined:

Now, the component of perpendicular to is obtained by vector subtraction:

Given that and , the expression for the remaining component is:

The orthogonal componentes of with respect to are and , respectively.

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.

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step-by-step explanation:

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