90 Degree Vector Sum

Geometry Level 1

Suppose there are two vectors $\vec{u}$ and $\vec{v}$ , where $|\vec{v}| = 16$ , $|\vec{u}| = 30$ , and the angle between the vectors is $90^\circ$ . What is $|\vec{u}+\vec{v}|?$

The answer is 34.

6 solutions

Andre Yudhistika
Jan 4, 2014

since the angle is 90 then cos 90=0

|u+v|=sqrt(|u|^2+|v|^2+2|u||v|cos90)

=sqrt(30^2+16^2)

=34

Siddhant Mahurkar
Apr 26, 2014

30²+16²=|u+v|² so, |u+v|=34

Hemanth Koundinya
Sep 12, 2015

|v|=16. |u|=30 |u+v|=sqrt(|v|^2+|u|^2+2(u.v) |u+v|=sqrt(16^2+30^2+16 30 cos90) |u+v|=sqrt(256+900+0) |u+v|=sqrt(1156) |u+v|=34

Koustav Mondal
Dec 19, 2013

|u+v|=( u^2+v^2+2uv*cos90)^(1/2)

={(30)^2+(16)^2}^(1/2)

=(900+256)^(1/2)

=1156^(1/2)

=34

Roman Roux
Apr 20, 2019

Pythagore : sqrt(16^2+30^2) = 34 (Vector are hypothenuse)

Leonhard Euler
Dec 15, 2013

We might be using vector notation, but this is a good old pythagorean distance problem. $a^2 + b^2 = c^2$

here are some free linear algebra books.

Keith Matthews, Elementary Linear Algebra, http://www.numbertheory.org/book/.

Jim Hefferon, Linear Algebra, http://joshua.smcvt.edu/linalg.html/.

Robert A. Beezer, A First Course in Linear Algebra, available free online at http://linear.ups.edu/.

90 Degree Vector Sum

The answer is 34.

6 solutions

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