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r & s are two vectors and |r| = 5. What is the value of |r+s| when s is perpendicular to (r+s) and |s| = 3?

Update:

Please show steps. Thanks in advance.

P.S. That's ''r'' not R.

2 Answers

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  • Yo
    Lv 4
    6 years ago
    Favorite Answer

    |r+s|^2 = (r+s) dot (r+s)

    = |r|^2 + 2 (r dot s) + |s|^2

    Given |r| = 5, and |s| = 3 we have:

    = 5^2 + 2 (r dot s) + 3^2

    = 34 + 2 (r dot s)

    since s is perpendicular to (r+s),

    s dot (r + s) = 0

    (s dot r) + |s|^2 = 0

    (s dot r) + 3^2 = 0

    (s dot r) = -9

    = 34 + 2(-9)

    = 16

    there:

    |r+s| = sqrt(16) = 4 <--- answer

  • 6 years ago

    |r+s| = 4.

    Note that r, s, & (r+s) form a "5-3-4" right triangle.........

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