Question

If a=i+6j+k and b=i+13j+k, find a unit vector with positive first coordinate orthogonal to both a and b.

Answer 1

Given any two vectors u and v, the cross product of them,
\[ u \times v \]
is orthogonal to both.

Answer 2

right did that....i got -7i + 7k

Answer 3

now if a vector u is orthogonal to v (nothing to do with u and v above), then u.v = 0.

But it's also true that (-u).v = 0.

Answer 4

right i checked with (a x b) * a = <-7,0,7> * <1,6,1> = -7+7 = 0

Answer 5

and (a x b) * b = <-7,0,7> * <1,13,1> = -7+7 = 0

Answer 6

No, what I'm saying is assuming u = -7i + 7k is indeed correct, then it orthogonal to the two original vectors. But so is -u.

Answer 7

which would be 7i - 7k?

Answer 8

yes

Answer 9

why is it being marked incorrect then?

Answer 10

because you need a unit vector

Answer 11

a unit vector in the direction 7i - 7k

Answer 12

awesome now i got it

Answer 13

thx dude