How do you normalize (i -2j + 3k) (i2j+3k)?

1 Answer
Dec 28, 2017

1/sqrt14(hati-2hatj+3hatk)114(ˆi2ˆj+3ˆk)

Explanation:

to normalize a vector means to change it to a unit vector, that is ensure that its magnitude is =1=1

hatveca=(veca)/|veca|ˆa=aa

we ahve

veca=hati-2hatj+3hatka=ˆi2ˆj+3ˆk

|a|14|a|14

=sqrt(1^2+2^2+3^2)=sqrt14=12+22+32=14

hatveca=1/sqrt14(hati-2hatj+3hatk)ˆa=114(ˆi2ˆj+3ˆk)