Find two unit vectors orthogonal to both < 1, -1, 1> and <0,4,4>?

Question

Calculus 3 Vectors: The Cross Product Section

Answer 1

HOMEWORK!!!

Take the cross product of these two vectors. This gives a vector normal to both. Now divide by it's length to get a unit vector with that property. Another is obtained by taking the negative of that one.

Answer 2

take the cross product of those two vectors, that gives you an orthongal vector to both of them, to make it a unit vector, divide by its norm.
the cross product of < 1, -1, 1> and <0,4,4> is: <-8,-4,4>, the unit vector therefore is:
1/√96<-8,-4,4>
the second unit vector would be the negative of the first.
-1/√96<-8,-4,4>

Answer 3

Take the cross product of the 2 vectors to get a vector
orthogonal to both.
I got <-8, -4, 4>. Now normalise it by dividing by its length.
This gives <-8, -4, 4>/sqrt(96).
Another unit vector can be obtained by taking
the negative of this one.

Answer 4

Cross product:

= [1, -1, 1] . [0, 4 , 4]
= [ -8 , -4 , 4]
= 4 [ -2, -1, 1]

Magnitude of cross product
= sq rt of { (-8)² + (-4)² + 4² }
= sq rt of 96

Therefore,
One of the unit vectors is (4/ sqrt 96) [ -2, -1 ,1]
i.e. ( [ -2, -1 ,1] / sqrt 6 )

And the other vector is the negative,
i.e. ( [ 2, 1, -1] / sqrt 6 )

Answer 5

X <0,4,4> = {-8,-4,4} magnitude 4?6, so unit vector is (a million/4?6) {-8,-4,4} <0,4,4> X = {8,4,-4} magnitude 4?6, so unit vector is (a million/4?6) {8,4,-4} you are going to be able to additionally use the dot product enable vector be {x, y, z}, then x - y + z = 0 4y + 4z = 0 enable any variable be a million, then you particularly can calculate x,y,z Then divide by using it somewhat is length to discover unit vector.

Answer 6

Last time I checked, I don't have any homework today.