If a = i +2j + k and b = i + 11j + k, find a unit vector with a positive first coordinate and orthogonal to both a and b.

Question

hartnn · Answer

can u take the cross product??

anonymous · Answer

yes ive done that and i got     -9i - 0j + 9k

hartnn · Answer

thats right.

anonymous · Answer

so how do i get the positive term?

hartnn · Answer

now ,lets just reverse the direction of that vector.
But still it will be orthogonal to both vectors , right?

reverse it by multiplying by -1

hartnn · Answer

what would u get?

anonymous · Answer

ok i see

anonymous · Answer

if i reverse the direction i get 9i - 0j - 9k and that isnt correct.

hartnn · Answer

9i-9k,that should be correct as its orthogonal to both vectors.

hartnn · Answer

how do u know 9i-9k isn't correct ?

anonymous · Answer

because my online homework wont accept that as my answer.

hartnn · Answer

O.o
UNIT vector!
can u find the magnitude of this vector?

anonymous · Answer

that would sqrt162 right?

hartnn · Answer

the magnitude of this vector is $9\sqrt2$
so divide this vector by $9\sqrt2$ and get the unit vector.

hartnn · Answer

yup sqrt162=9sqrt 2

anonymous · Answer

thats not right either though.. its asking for the answer in the form ikj

hartnn · Answer

is sqrt2 allowed?
if yes,then:
i/(sqrt2)+0j-k/sqrt(2)
else replace it by 0.707

hartnn · Answer

0.707i +0j-0.707k

hartnn · Answer

got accepted?

anonymous · Answer

yes it did thanks!

hartnn · Answer

welcome :)