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 x. Is the resulting vector perpendicular to the given vectors?

A.; yes

B.; no

C.; yes

D.; no

1.

v x w = 8 i - 24 j + 15 k + 10 j - 12 i - 24 k =

= - 4 i - 14 j - 9 k

Answer: D)

2.

v x w = - 16 i - 16 j - 18 k + 12 j + 48 i - 8 k =

= 32 i - 4 j - 10 k

Answer: C)

3.

The cross product:

x =

= - 21 i + 16 j - 30 k - 18 j - 10 i - 56 k =

= - 31 j - 2 j - 86 k =

Vectors are perpendicular if: cos (u, v) = 0

* = 186 - 14 - 172 = 0

* = - 248 - 10 + 258 = 0

Answer: A), yes.