Consider the points P(5,5,1) and Q(13,13,3). a. Find PQ with right arrow and state your answer in two forms: (a, b,c) and ai+bj+ck.
b. Find the magnitude of PQ with right arrow.
c. Find two unit vectors parallel to PQ with right arrow.

a) or , b) The magnitude of segment PQ is approximately 11.489, c) The two unit vectors associated to PQ are, respectively: and

Step-by-step explanation:

a) The vectorial form of segment PQ is determined as follows:

Where and are the respective locations of points Q and P with respect to origin. If and , then:

Another form of the previous solution is .

b) The magnitude of the segment PQ is determined with the help of Pythagorean Theorem in terms of rectangular components:

The magnitude of segment PQ is approximately 11.489.

c) There are two unit vectors associated to PQ, one parallel and another antiparallel. That is:

(parallel) and (antiparallel)

The unit vector is defined by the following equation:

Given that and , the unit vector is:

The two unit vectors associated to PQ are, respectively:

and

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step-by-step explanation:

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