Essentials of University Mathematics Example 3. Find the length of the vector PQ from the point P(3.-5. 2) to the point QC

Question

Essentials of University Mathematics
Example 3.
Find the length of the vector PQ from the point P(3.-5. 2) to the
point QC-5.4.9)
Find a unit vector with the direction of PQ

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Trúc Chi 4 years 2021-08-27T22:06:20+00:00 1 Answers 9 views 0

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  1. Dau
    0
    2021-08-27T22:07:35+00:00
    Reply

    Answer:

    The length of the vector is of \sqrt{194}

    The unit vector with the direction of PQ is (\frac{8}{\sqrt{194}}, \frac{9}{\sqrt{194}}, \frac{7}{\sqrt{194}}

    Step-by-step explanation:

    Vector from point P(3,-5,2) to Q(-5,4,9)

    The vector is:

    PQ = Q - P = (-5-3, 4-(-5), 9-2) = (8,9,7)

    The length is:

    \sqrt{8^2+9^2+7^2} = \sqrt{194}

    The length of the vector is of \sqrt{194}

    Find a unit vector with the direction of PQ

    We divide each component of vector PQ by its length. So

    (\frac{8}{\sqrt{194}}, \frac{9}{\sqrt{194}}, \frac{7}{\sqrt{194}}

    The unit vector with the direction of PQ is (\frac{8}{\sqrt{194}}, \frac{9}{\sqrt{194}}, \frac{7}{\sqrt{194}}

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )