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Perpendicular Vectors:

Find v x w if v=5i -4j +4k & w=-6i +3j -2k.

A3i-4j-2k
B-14i-9j-4k
C5i +3j -4k
D-4i -14j -9k

Find v x w if v=-3i-4j-8k & w=2i+6j+4k.

A12i -2j +3k
B8i +12j +32k
C32i -4j -10k
D10 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

Verified Answer :

HomertheGenius

  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:
    < - 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
    Answer: A ) < - 31, - 2 , - 86 >,  yes.

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