Question

Find two unit vectors orthogonal (perpendicular) to both the given vectors:

Answer 1

<1, -1, 1>
<0, 4, 4>

Answer 2

find the det.

Answer 3

i was thinking a cross product meself

Answer 4

ahh, "determinant" ... yeah

Answer 5

oh yeah, cross product. Lol. if it equals 1, it's orthogonal.

Answer 6

My work:
Found determent of following matrix:
i j k
1 -1 1
0 4 4
\[=-8i -4j + 4k\]

and:
i j k
0 4 4
1 -1 1
\[=8i + 4j - 4k\]

So, translate to unit vectors you should have:
<-1, -1, 1> and <1, 1, -1>

Answer 7

8,4,4 doesnt reduce to 1,1,1

Answer 8

unit vector

Answer 9

and 1,1,1 is sqrt3 long, not 1 long

Answer 10

ah, that's probably what I'm doing wrong..

Answer 11

<1, -1, 1>
<0, 4, 4>

x 0 1
y 4 -1
z 4 1

x = (4--4)
y = -(0-4)
z = (0-4)

(8,4,-4) is normal to both ... we can reduce by a factor of 4

(2,1,-1) , now divide it by its length

Answer 12

+- (2,1,-1)
----------
sqrt6

Answer 13

thanks