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.

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step-by-step explanation: