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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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|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

• |r+s| = 4.

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

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