Prove that the vectors A=6i+9j-12k and B=2i+3j-4k are parallel.

Two vectors are said to be parallel when their cross product is zero.So,A×B =6i+9j-12k × 2i+3j-4k          = ijk69-1223-4         =(-36 +36) i^ --24 + 24 j^ + 18-18 k^         = 0So as their cross product is zero so we can call them as parallel vectors.

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The slope of both the vectors are equal so they are parallel.

Slope = tanΘ

tanΘ = y/x

tan Θ = 3/2 for both the vectors.

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