(a) u × v
(b) v × u
(c) v × v
(a) u × v = (-4 + 4)i - (4 + 4)j + (4 + 4)k
= 0 i - 8j + 8k
(b) v × u = (-4 + 4)i - (-4 - 4)j + (-4 - 4) k
= 0i + 8i - 8k
(c) v × v = (16 - 16)i - (16 - 16)j + (16 - 16)k
= 0i - 0j + 0k
= 0
Not sure what is stopping you from using the formula.
The x component of u x v is (uy*vz - vy*uz) = (-1)*4 - 4*(-1). Just plug in the numbers.
And do the same for (u x v)_y = (uz*vx - vz*ux) and (u x v)_z = (ux*vy - vx*uy). Just plug in.
v x u is the negative of u x v. True for any two vectors.
v x v is 0. True for any vector.
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Answers & Comments
(a) u × v = (-4 + 4)i - (4 + 4)j + (4 + 4)k
= 0 i - 8j + 8k
(b) v × u = (-4 + 4)i - (-4 - 4)j + (-4 - 4) k
= 0i + 8i - 8k
(c) v × v = (16 - 16)i - (16 - 16)j + (16 - 16)k
= 0i - 0j + 0k
= 0
Not sure what is stopping you from using the formula.
The x component of u x v is (uy*vz - vy*uz) = (-1)*4 - 4*(-1). Just plug in the numbers.
And do the same for (u x v)_y = (uz*vx - vz*ux) and (u x v)_z = (ux*vy - vx*uy). Just plug in.
v x u is the negative of u x v. True for any two vectors.
v x v is 0. True for any vector.