What is #||v||# if #v = < 3,1,-2 >#? Precalculus 3-D Cartesian Coordinate System Vectors in Space 1 Answer Bill K. Jul 15, 2015 #sqrt(14)\approx 3.74166# Explanation: The length #||vec(v)||# of a 3-dimensional vector #\vec(v)=\langle a,b,c\rangle# is #sqrt(a^2+b^2+c^2)#. Therefore if #vec(v)=\langle 3,1,-2\rangle#, then #||vec(v)||=sqrt{9+1+4}=sqrt(14)\approx 3.74166# Answer link Related questions How do vectors represent a point in space? How do I know if two vectors are equal? What is the magnitude of vector #AB# if #A= (4,2,-6)# and #B=(9,-1,3)#? How do I find the unit vector for #v = < 2,-5,6 >#? How do I find the dot product of two three-dimensional vectors? How do I find the angle between two vectors in three-dimensional space? What does it mean if two vectors are orthogonal to each other? What are the standard three-dimensional unit vectors? How could I determine whether vectors #P< -2,7,4 >, Q< -4,8,1 >#, and #R< 0,6,7 ># are all in... How do you find the equation of the plane in xyz-space through the point #p=(4, 5, 4)# and... See all questions in Vectors in Space Impact of this question 2350 views around the world You can reuse this answer Creative Commons License