Perpendicular vectors:
find v x w if v=5i -4j +4k & w=-6i +3j -2k.
a. 3i-4j-2k
b. -14i-9j-4k
c. 5i +3j -4k
d. -4i -14j -9k
find v x w if v=-3i-4j-8k & w=2i+6j+4k.
a. 12i -2j +3k
b. 8i +12j +32k
c. 32i -4j -10k
d. 10 i -8j +3k
find the cross product < -6, 7, 2> x < 8, 5, -3> . is the resulting vector perpendicular to the given vectors?
a. < -31,-2,-86> ; yes
b. < -37,-2,0> ; no
c. < 0,-86,-37> ; yes
d. < -37, 0, -80> ; no

1.
v x w = 8 i - 24 j + 15 k + 10 j - 12 i - 24 k =
= - 4 i - 14 j - 9 k
D )
2.
v x w = -16 i - 16 j - 18 k + 12 j + 48 i - 8 k =
= 32 i - 4 j - 10 k
C )
3.
The cross product:
< - 6, 7, 2 > x < 8, 5, -3 > =
= - 21 i + 16 j - 30 k - 18 j - 10 i - 56 k =
= - 31 j - 2 j - 86 k = < - 31, - 2, - 86 >
Vectors are perpendicular if: cos ( u, v ) = 0
< - 6 , 7. 2 > * < -31, - 2, - 86 > = 186 - 14 - 172 = 0
< 8, 5 , - 3 > * < - 31, - 2, - 86 > = -248 - 10 + 258 = 0
A ) < - 31, - 2 , - 86 >,  yes.