Question

Find a unit vector in the same direction as a = 6 I − 2 J − 2 K.

? I + ? J + ? K (Note that, a unit vector is a vector whose length is 1. Multiplying any non-zero vector V by 1/|V| produces a unit vector, and multiplying any unit vector by -1 shows that there are two unit vector which are multiples of any non-zero vector. )

Answer 1

divide by sqrt(44)

Answer 2

devide each one by sqrt of 44 ?!

Answer 3

it gives (3I-J-K)/sqrt(11)

Answer 4

yes

Answer 5

i'm lost !

Answer 6

OK, they want you to scale the vector so that its magnitude is 1, the magnitude is given by sqrt(a²+b²+c²),

Answer 7

so if your vector has the magnitude sqrt(6²+(-2)²+(-2)²), you should divide it by that,

Answer 8

after simplifying it gives (3I-J-K)/sqrt(11)

Answer 9

So you start with vector <6,-2,-2> and to make it a unit vector you divide each component by the length of this vector (i.e., sqrt44=2*sqrt11). This gives:\[<3/ \sqrt11,-1/\sqrt11,-1/\sqrt11>\]If you compute the length of this unit vector you will see that it comes out to length one as required. You can also write this vector as\[\frac {3}{\sqrt11}i +\frac {-1}{\sqrt 11}j+\frac {-1}{\sqrt11}k\]

Answer 10

thanks so much ! to u all for the answer